WO1996021968A1

WO1996021968A1 - System and method for digital fm demodulation

Info

Publication number: WO1996021968A1
Application number: PCT/US1995/012415
Authority: WO
Inventors: Kevin H. Peterson; Henry Massalin
Original assignee: Microunity Systems Engineering, Inc.
Priority date: 1995-01-12
Filing date: 1995-09-29
Publication date: 1996-07-18
Also published as: AU3729895A

Abstract

A digital FM demodulator and method for determining phase changes in highly oversampled complex FM digital signals is described. In a first embodiment the FM signal is oversampled with respect to the frequency of its associated modulating signal. In this embodiment a first digital processing stage delays and conjugates the original FM signal. This delayed conjugated original FM signal is then multiplied with the original FM signal to generate a second signal that represents the changes in the phase between samples of the original FM signal. A second processing stage then delays and conjugates the second signal. The delayed conjugated second signal is then multiplied with the original second signal to generate a third signal that represents changes in the phase between samples of the second signal. The imaginary component of the third signal is passed through a digital integrator which outputs the phase changes of the original FM signal. In a second embodiment, the highly oversampled signal is oversampled with respect to the deviation frequency of its associated modulating signal. In this embodiment the center frequency of the original FM signal is frequency shifted to approximately zero frequency. This frequency shifted signal is then delayed and conjugated. The delayed conjugated shifted signal is then multiplied with the original frequency shifted signal; yielding an output signal where the imaginary portion of the output signal is equal to the phase changes of the original FM signal.

Description

SYSTEM AND METHOD FOR DIGITAL FM DEMODULATION

FIELD OF THE INVENTION

The present invention relates to the field of digital signal processing, and particularly to digital FM demodulation. BACKGROUND OF THE INVENTION

In the field of communications, an analog carrier signal is often frequency modulated to transmit audio information, e.g. FM radio and television sound. To frequency modulate a carrier signal is to add a time varying phase component to the carrier in which the changes in phase correspond directly to the information signal, (i.e. the modulating signal) being transmitted. A frequency modulated analog carrier is represented

mathematically as:

where ω_ct is the carrier frequency term and ø(t) is the time varying phase term. The changes in ø(t) (or equivalently the first derivative dø(t)/dt) constitute the modulating signal.

At the receiver, an FM demodulator functions to detect the changes in the phase term of the modulated carrier and thereby extracts the transmitted modulating signal. FM demodulators may be implemented using either analog or digital signal processing techniques. When implementing a digital FM demodulator, it is first necessary to convert the FM analog signal into an FM digital signal in order to perform the digital demodulation steps. This is achieved with an analog-to-digital (A/D) converter. The A/D converter samples the FM analog signal at some given rate, commonly referred to as the sample rate or sampling frequency (f_s), to generate an FM digital signal corresponding to the original analog signal. A frequency modulated digital carrier is represented mathematically as a function of discrete sample indices:

where ω_cn is the carrier frequency term, φ[n] is the time varying phase term and n is the sample index.

Frequency modulated carrier signals are typically parameterized in terms of two components, frequency deviation (f_d) and frequency of modulation (f_m). Frequency deviation (f_d) specifies the maximum extent of the carrier's deviation from its nominal center frequency and f_m specifies the maximum rate at which this deviation occurs. In the case in which the modulating signal is a simple sinusoid, f_d corresponds to the maximum amplitude of the sinusoid, i.e.

If the modulating signal is not a simple sinusoid, then f_m corresponds to the maximum frequency component present in the modulating signal.

A well known digital signal processing theorem, referred to as the

Nyquist theorem, states that in order to represent precisely all of the

information in an analog signal, the sample rate (f_s) of the A/D converter must be at least twice that of the Nyquist frequency (f_N) of the analog signal, i.e. f_s ≥ 2f_N. The Nyquist frequency is the maximum frequency in the analog signal beyond which no significant energy (information) is present.

In the case in which a digital signal is generated by sampling an analog signal at a rate much greater than twice the Nyquist frequency, i.e. f_s > > 2f_N, the resultant digital signal is referred to as a highly oversampled digital signal. The degree of oversampling may be termed the oversampling factor (N). In other words, instead of f_s being twice the Nyquist frequency of the analog signal, f_s is two times the Nyquist frequency times the oversampling factor, i.e. f_s≥ 2Nf_N.

The present invention is a simple digital FM demodulator and method of demodulation that operates on highly oversampled signals. A consequence of high oversampling is that even the most rapid changes in a signal's amplitude are represented with many samples closely spaced in time - the differences in amplitude of which are very small. The small size of these differences makes possible certain approximations that enable the digital FM demodulator of the present invention.

SUMMARY OF THE INVENTION

A digital FM demodulator and method for phase detection of highly oversampled complex signals is described. In the first method and embodiment of the present invention the oversampling factor N is specified with respect to the frequency of the modulating signal f_m, i.e. f_s≥ 2Nf_m. In this

embodiment, the highly oversampled complex signal that is to be demodulated (the first signal) is processed to generate a second signal that represents the change in the phase between successive samples of the first signal. Next, the second signal is processed to generate a third signal which represents the change in phase between successive samples of the second signal. Finally the imaginary component of the third signal is digitally integrated in order to determine the change in phase of the first signal.

Second and third signals are processed in the following manner. First, the original complex digital signal is passed through a first signal delay unit to delay the original signal by one sample delay. Next, the delayed original signal is passed through a first complex conjugate block to obtain the complex conjugate of the delayed original signal. A first complex multiplier multiplies the complex conjugate of the delayed original signal with the original signal yielding a second signal.

The second signal is then delayed and conjugated by passing it through a second delay unit and then a second complex conjugate unit. These operations yield a signal that is the complex conjugate of the delayed second signal. A second multiplier multiplies the complex conjugate of the delayed second signal with the original second signal to provide a third signal. Next, the third signal is processed through a means for determining the imaginary part of the third signal. This operation yields digital data that represents changes in the change of phase of the original highly oversampled FM digital signal. A digital integrator continuously adds this digital data yielding a signal that represents changes in the phase of the original FM modulated signal. In one embodiment, the digital integrator comprises an adding unit and a third delay unit.

In a second embodiment of the present invention, the oversampling factor N is specified with respect to the frequency deviation f_d of the modulating signal, i.e. f_s≥ 2Nf_j. In this embodiment, the original FM modulated signal is passed through a mixer so as to generated a frequency shifted original FM modulated signal centered at approximately zero frequency. The frequency shifted original FM modulated signal is passed through a delay unit and a complex conjugate unit to generate a second signal that represents the frequency shifted, delayed and conjugated signal of the original FM modulated signal. The frequency shifted original FM modulated signal and the second signal are multiplied by a complex multiply unit to generate a third signal. The imaginary portion of this third signal is equal to the changes in phase of the original FM modulated signal.

In both of the embodiments of the present invention, the original complex digital signal is characterized as having an oversampling factor approximately greater than or equal to 18 with respect to both parameters of the modulating signal, f_d and f_m, in order to obtain a worst case error factor of less than -60 dB (i.e. 1 × 10^-3) in the phase change signal. BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a typical FM demodulation system including an FM demodulator.

Figure 2A illustrates a typical multi-channel real signal. Figure 2B illustrates the multi-channel complex signal shown in Figure 2A after being processed by complex mixer 10 in Figure 1.

Figure 2C illustrates the multi-channel signal after it has been mixed and preselected. Figure 3 illustrates a first embodiment of the digital FM demodulator of the present invention.

Figure 4 is a flowchart illustrating a first method of the present invention.

Figure 5 illustrates a second embodiment of the digital FM demodulator of the present invention.

Figure 6 is a flowchart illustrating a second method of the present invention.

DETAILED DESCRIPTION

A digital FM demodulator and method for phase detection of highly oversampled complex signals is described. In the following description, numerous specific details are set forth, such as oversampling factors, error factors etc., in order to provide a thorough understanding of the present invention. It will be obvious, however, to one skilled in the art that these specific details need not be employed to practice the present invention. In other instances, well-known digital signal processing theory has not been described in detail in order to avoid unnecessarily obscuring the present invention.

Figure 1 illustrates the basic elements employed in a digital FM demodulation system for processing an input analog signal a(t). Generally, in the field of communications, signal a(t) comprises a collection of analog channels, each channel n having some center frequency, f_n, and a

corresponding bandwidth Δf_n, respectively (Figure 2A).

Signal a(t) having a frequency magnitude | A(f) | is coupled to the input of complex mixer 10 (Figure 1). Signal a(t) comprises many channels at center frequencies: f_n-1 f_n, and f_{n+ 1} , in addition to other channels not shown in Figure 2A. Mixer unit 10 shifts signal a(t) so that the channel of interest having center frequency f_n is centered at some intermediate frequency f_i, (where f_j is chosen to enable preselection). Mixing is performed in order to make practical the subsequent step of preselection and A/D conversion. As shown in Figure 1, carrier frequency f_c, generated by oscillator 9, is coupled to mixing unit 10 along with input signal a(t). The result of mixing signal a(t) to intermediate frequency fj by carrier f_c is a complex signal b(t) (Figure 2B) having a real component b_r(t) and an imaginary component b_i(t) and having a frequency magnitude | B(f) | . As can be seen, the channel of interest is shifted to f_i = f _n - f_c .

Each of the real and imaginary components of b(t) are coupled to corresponding preselect units 11 and 12, respectively. Preselect units 11 and 12 filter out all other channels except for the channel of interest, as illustrated in Figure 2C. Preselect unit 11 generates the real component c_r(t) of a signal c(t) and preselect unit 12 generates the imaginary component c_i(t) of c(t).

The next step of the FM demodulation system shown in Figure 1 is the analog-to-digital (A/D) conversion of each of the real and imaginary

components of signal c(t). A/D converters 13 and 14, perform the conversions by taking discrete samples of the real and imaginary components of signal c(t) at a specific rate. For a given channel having a bandwidth Δf_n, f_s needs to be at least twice the bandwidth of the channel, (i.e. f_s≥ 2Δf_n).

For purposes of a first embodiment of the present invention the sampling rate is increased by an oversampling factor N, where N is specified with respect to the frequency of the modulating signal f_m, i.e. f_s≥ 2Nf_m.

Alternatively, in the second embodiment of the present invention the sampling rate is increased by an oversampling factor N, where N is specified with respect to the frequency deviation f^ of the modulating signal, i.e. f_s≥ 2Nf_d.

It should further be noted that in order for the FM demodulator of the present invention to provide the desired result, the output of mixer 10 must yield a complex signal having both imaginary and real components.

The digitally converted imaginary and real components of c(t),

(designated as a_i[n] and a_r[n]) are coupled to FM demodulator 15 of the present invention. FM demodulator 15 functions to extract the information encoded in the digital frequency modulated signal provided by A/D converters 13 and 14 by detecting the change in phase, Aø[n], of digital signal a[n], where Δø[n] = ø[n] - ø[n-1] and,

where ø[n] is the phase term of the signal, ω_cn is the carrier frequency, n is the sample indicator, and A is the magnitude of the signal. For purposes of the present invention it is assumed that A is approximately equal to 1. Input signal a[n] is characterized as a complex signal including real and imaginary components.

Typically, after detection, the detected phase change digital signal∆ø[n] is then subjected to additional audio processing (unit 16, Figure 1) and then converted back to an analog signal by digital-to-analog (D/A) converter 17. Once in analog form, the detected phase change signal constitutes the desired audio signal that was encoded in the original transmitted signal (assuming no other audio processing modifications).

In concept, the first embodiment of the FM demodulator 15 illustrated in Figure 3 and a corresponding method of the present invention determines the change in phase of a[n] by first determining a signal b[n] that represents the change in phase between two successive samples of digital signal a[n]. Next, the demodulator of the present invention determines a signal c[n] that represents the change in the phase between two successive samples of digital signal b[n]. Finally, the imaginary portion of signal c[n] is digitally integrated to generate ∆ø[n] in the case in which a[n] is a highly oversampled digital signal where the oversampling factor N is specified with respect to the frequency of the modulating signal f_m such that f_s≥ 2Nf_m.

Figure 3 shows a first embodiment of the FM demodulator 15 of the present invention. As shown in Figure 3 input signal a[n] is coupled to the input of FM demodulator 15. Referring to Figure 3, a[n] is passed through delay unit 18. Unit 18 delays signal a[n] by one sample delay, so as to generate signal a[n-1]. In vector polar notation signal a[n-1] is shown below by equation 2.

One manner in which delay unit 18 may be implemented is with a digital register that holds each sample for a period equal to one sampling interval.

After delaying a[n], complex conjugate unit 19 negates the exponent component of a[n-1], or equivalently negates the instantaneous phase angle of the complex vector of a[n-1]. This operation is indicated by equation 3.

In the next step, digital multiplier 20 multiplies the original signal a[n] with the delayed complex conjugate signal a[n-1] to generate a second signal b[n] as shown below by equation 4.

By setting the term ø[n] - ø[n-1] equal to∆ø[n], i.e.∆ø[n] = ø[n] - ø[n-1], and substituting this into b[n], b[n] becomes:

Signal b[n] represents the change in the phase between two successive samples of signal a[n] but includes a constant term proportional to the carrier frequency ω.

Next, signal b[n] is delayed by unit 21 and then processed through complex conjugate unit 22 as was previously done with signal a[n]. Equations 6 and 7 illustrate these two processing steps.

Complex digital multiplier unit 23 functions to multiply original signal b[n] with b[n-1] to generate a third signal c[n] as indicated by equation 8.

Using a well know mathematical relationship, c[n] may be represented as shown below in equation 9.

where cos {Δø[n] - Aø[n-1]} is the real portion of c[n] and sin {Δø[n] - Aø[n-1]} is the imaginary portion of c[n]. Signal c[n] represents the change in the phase between two successive samples of signal b[n]. Unit 24 functions to select the imaginary component of c[n] as shown below by equation 10. eq.10 Imaginary portion of c[n] = Im{ c[n] } = sin {Δø[n] -∆ø[n-1]} For a frequency modulated digital signal, the change in phase∆ø[n] represents the instantaneous amplitude of the modulating signal. Further, changes in the change of phase, that is∆ø[n] -∆ø[n-1], represent changes in the amplitude of the modulating signal. In the case in which a[n] is a highly oversampled signal with respect to the modulating frequency, i.e. f_s » 2f_m, ∆ø[n] - Δø[n-1] is very small and thus, for the present invention is

approximated to be zero (where f_m is the maximum frequency present in the modulating signal). Using the well know mathematical approximation, Sin{a} ≈ a, for a≈ 0, equation 10 is approximated to be:

for Δø[n] -∆ø[n-1] - 0.

The output of unit 24 (Figure 3) is coupled to digital integrator 25 which continuously sums all the changes in the change of phase,∆ø[n] -∆ø[n-1], and outputs the desired resultant, i.e. the change of phase,∆ø[n], of a[n].

Mathematically this is represented as shown in equation 12:

where k is the index of summation. It should be noted that digital integrator 25 may be implemented utilizing digital adder 26 along with a delay unit 27 as shown in Figure 3.

It should be further noted that since in the embodiment shown in Figure

3 a[n] is a highly oversampled signal, where f_s≥ 2Nf_m the present invention assumes the expression sin {a}≈ a to be true. In other words, the worst case error factor, (the difference between sin {a} and a), is approximately equal to zero, as shown below in equation 13. eq.13 worst case error factor = | sin {a} - a | <■» 0, when f_s≥ 2Nf_m, i.e. when a≈ 0. As N decreases, however, the worst case error factor increases such that | sin {a} - a | ≈ 0. The relationship between oversampling factor N and the worst case error factor (related in dB) is shown below in Table 1 for the above equation.

As can be seen in Table 1, in order for the error factor of∆ø[n] to be less than -60 dB, (i.e. 1 × 10^-3), oversampling factor N of input signal a[n] needs to be greater than or equal to 18. Similarly for a worse case error factor less than -77 dB, N needs to be greater than 34. For purposes of this invention, a -60 dB error is considered acceptable. Thus, the present invention provides accurate phase differences when demodulating a highly oversampled signal having an oversampling factor of N greater than 18.

It should be noted that the present invention may also be utilized with an input FM digital signal having an oversampling factor N less than 18. In this case however, the phase change information provided by the FM demodulator of the present invention would have a worse case error factor greater than -60 dB and thus would provide less accurate phase change information.

It should also be noted that the operations performed by digital complex multiplier 23 and unit 24 may be consolidated into a digital multiplication operation that only computes the imaginary component of c[n] when multiplying b[n] and b[n-1]*, (instead of performing the full multiplication operation that multiplies b[n] with b[n-1]* to determine both the real and imaginary components of c[n]). Thus, in another embodiment of the present invention, unit 24 may be eliminated if digital complex multiplier 23 is designed to compute only the imaginary component of c[n] when given b[n] and b[n-1]*.

Figure 4 illustrates the steps of a first method of the present invention corresponding to Figure 3. Initially, memory storage is designated for signals a[n], b[n], c[n], and d[n] for sample indexes n-0 and n-1, (where a signal having a sample index value n-1 occurs one sample delay later than the same signal having a sample index value n-0). For the flow chart illustrated in Figure 4, a0 corresponds to a[n] and a1 corresponds to a[n-1]. Similarly, b0 corresponds to b[n] and b1 corresponds to b[n-1], c0 corresponds to c[n] and cl corresponds to c[n-1], d0 corresponds to d[n] and dl corresponds to d[n-1].

Also indicated by Figure 4 initial conditions a₁, b₁, and c₁ = 0 are established. In other words, memory elements a₁, b₁ , and c₁ are empty since they represent past samples.

After establishing the initial conditions, a first sample a0 of a[n] is acquired. Next, b0 is computed. The method for determining b0 is to separately compute the real (i.e. b0.r) and the imaginary (i.e. b0.i) components of b0. These formulas incorporate the complex conjugate operation (block 19) and the complex multiply operation, (block 20) as shown in Figure 3. It should be noted that in the initial computation of b0.i and b0.r, a1 is zero. However after the first determination of b0, a1 is set to a0. In other words, the signal sample a1 is set to the previous signal sample (a0).

After determining b0, the imaginary component (c0.i) of c0 is computed. The reason that only the imaginary component is determined is because the real component of c0 is not needed in the rest of the steps of this method of the present invention. The determination of c0.i incorporates the complex conjugate operation (block 22) and the complex multiply operation, (block 23) as shown in Figure 3. After c0.i is computed, b0 is set to bl.

Finally, d0 is determined by adding the imaginary component c0.i to the previous d0 and lastly, d0 is outputted. It should be noted that initially, d1 is equal to zero since it has not yet been determined. Thus, c0.i is added to zero on the first pass of steps to determine d0. When dl is set equal to d0 in the first pass, dl is a non-zero value in the second and subsequent other passes through the steps shown in Figure 4. As shown in Figure 4, after determining d0, a new a0 value is obtained so as to generate a new d0 value.

As described in conjunction with the embodiment shown in Figure 3, a[n] is a highly oversampled signal where oversampling factor N is specified with respect to the frequency of the modulating signal, i.e. f_s≥ 2Nf_m.

Specifying the oversampling factor in this manner allows for the assumption that sin {∆ø[n] -∆ø[n-1]}≈ Δø[n] - Δø[n-1] which consequently facilitates the first embodiment of the present invention shown in Figure 3. In contrast, the second embodiment of the present invention shown in Figure 5 assumes that a[n] is a highly oversampled signal where oversampling factor N is specified with respect to the deviation frequency of the modulating signal, i.e. f_s≥ 2Nf_d. Specifying the oversampling factor in this manner facilitates the implementation of the second embodiment of the present invention by allowing for the assumption that sin{Δø[n]} = Δø[n].

In the second embodiment of the present invention shown in Figure 5 oversampled signal a[n] (equation 1) is coupled to complex digital mixer 28 along with mixing frequency f_i. As was described in conjunction with the system shown in Figure 1, a[n] is a complex digital signal centered at a center frequency f_i, where f_i is a non-zero frequency.

Mixer 28 functions to shift the center frequency of signal a[n] to zero frequency thereby making the carrier frequency of the modulating signal approximately equal to zero, i.e. ω_c = 0. Signal a'[n] designates the frequency shifted a[n] and is represented mathematically by equation 14 as shown below.

Signal a'[n] is then passed through delay unit 29 and complex conjugate unit 30, yielding a delayed complex conjugate signal of a'[n] as indicated by equation 15 below.

The above signal is multiplied with signal a'[n] by digital multiplier 31 resulting in complex digital signal b[n]. The digital multiplication performed by multiplier 31 is shown below by equation 16.

By setting the term ø[n] - ø[n-1] equal to Δø[n], i.e.∆ø[n] = ø[n] - ø[n-1], and substituting this into b[n], b[n] becomes:

Using a well know mathematical relationship, b[n] may be represented as shown below in equation 17.

where cos {Δø[n]} is the real portion of b[n] and sin {Δø[n]} is the imaginary portion of b[n]» Unit 32 functions to select the imaginary component of b[n] as shown below by equation 19.

Thus a signal equal to sin {Δø[n]} is seen at the output of unit 32. Using the mathematical approximation, sin{a}≈ a, for a≈ 0, equation 19 is approximated to be:

for∆ø[n]≈ 0. In other words, the output of unit 32 yields the desired resultant, i.e. the change of phase, Δø[n], of a[n].

As with the previous embodiment shown in Figure 3, the operations performed by digital complex multiplier 31 and unit 32 may be consolidated into a digital multiplication operation that only computes the imaginary component of b[n] when multiplying a'[n] and a'[n-1]*. Thus, in another embodiment of the present invention, unit 32 may be eliminated if digital complex multiplier 31 is designed to compute only the imaginary component of b[n] when given a'[n] and a'[n-1]*.

Figure 6 illustrates the steps of a second method of the present invention corresponding to Figure 5. Initially, memory storage is designated for signal a[n] for sample indexes n-0 and n-1 and for signal b[n] for sample index n-0. For the flow chart illustrated in Figure 6, a0 corresponds to a[n] and a1 corresponds to a[n-1]. Similarly, b0 corresponds to b[n]. Also indicated by Figure 6 is the initial condition a1 = 0, i.e. memory element a1 is empty.

After establishing the initial condition, a first sample a0 of a[n] is acquired. Next, this sample is mixed with complex carrier at a frequency f_i in order to frequency shift the sample to approximately zero frequency. Next, the imaginary component (b0.i) of b0 is computed by multiplying the frequency shifted signal a'[n-0] with the shifted, delayed and conjugated signal a'[n-1]*. The reason that only the imaginary component of b0 is determined is because the real component is not needed in the rest of the steps of this method of the present invention. The determination of b0.i incorporates the operations of delay unit 29, complex conjugate unit 30 and complex multiply unit 31 as shown in Figure 5. Since only the imaginary portion of b0 is computed, the performance of block 32 (Figure 5) is obviated from this method.

As indicated in Figure 6, b0.i is equal to the desired resultant phase change signal∆ø[n] due to the approximations described above. Finally, a1 is set to a0, the phase change signal∆ø[n] is outputted to the next stage of audio processing (block 16, Figure 1), and a new a0 is obtained to generate a new ∆ø[n] value.

Although the elements of the present invention have been described in conjunction with a certain embodiment, it is appreciated that the invention may be implemented in a variety of other ways. Consequently, it is to be understood that the particular embodiment shown and described by way of illustration are in no way intended to be considered limiting. Reference to the details of these embodiments is not intended to limit the scope of the claims which themselves recite only those features regarded as essential to the invention.

Claims

CLAIMS I Claim:

1. An FM digital demodulator for determining phase changes in an FM digital complex signal having an associated modulating signal and an associated sampling frequency, said modulating signal having an associated modulating frequency, said FM digital complex signal being highly

oversampled wherein said sampling frequency is much greater than said modulating frequency times an oversampling factor N, said FM digital demodulator comprising:

a first means for delaying said FM digital complex signal by one sample delay so as to generate a delayed FM digital complex signal;

a first means for negating the phase of said delayed FM digital complex signal so as to generate the complex conjugate of said delayed FM digital complex signal;

a first means for digitally multiplying said FM digital complex signal with said complex conjugate of said delayed FM digital complex signal to generate a second digital signal;

a second means for delaying said second digital signal by one sample delay so as to generate a delayed second digital signal;

a second means for negating the phase of said delayed second digital signal so as to generate the complex conjugate of said delayed second digital signal;

a second means for digitally multiplying said second digital signal with said complex conjugate of said delayed second digital signal to generate a third digital signal, said third digital signal having a real and an imaginary

component;

a means for determining said imaginary component of said third digital signal; a means for digitally integrating said imaginary component of said third digital signal, said digital integrating means outputting a signal corresponding to said phase changes in said FM digital signal.

2. The digital demodulator as described in Claim 1 wherein said oversampling factor is approximately equal to 18 and said FM digital demodulator determines said phase changes with an associated worst case error factor of less than or equal to -60 dB.

3. An FM digital demodulator for determining phase changes in an FM digital complex signal having an associated modulating signal and an associated sampling frequency, said modulating signal having an associated modulating frequency, said FM digital complex signal being highly

a second means for negating the phase of said delayed second digital signal so as to generate the complex conjugate of said delayed second digital signal; a second means for digitally multiplying said second digital signal with said complex conjugate of said delayed second digital signal to generate an imaginary component of a third digital signal;

a means for digitally integrating said imaginary component of said third digital signal, said digital integrating means outputting a signal corresponding to said phase changes in said FM digital signal.

4. The digital demodulator as described in Claim 3 wherein said oversampling factor is equal to 18 and said FM digital demodulator determines said phase changes with an associated worst case error factor of less than or equal to -60 dB.

5. A method of determining phase changes in an FM digital complex signal having an associated modulating signal and an associated sampling frequency, said modulating signal having an associated modulating frequency, said FM digital complex signal being highly oversampled wherein said sampling frequency is much greater than said modulating frequency times an oversampling factor N, said method comprising the steps of:

delaying said FM digital complex signal by one sample delay so as to generate a delayed FM digital complex signal;

negating the phase of said delayed FM digital complex signal so as to generate the complex conjugate of said delayed FM digital complex signal; digitally multiplying said FM digital complex signal with said complex conjugate of said delayed FM digital complex signal to generate a second digital signal;

delaying said second digital signal by one sample delay so as to generate a delayed second digital signal;

negating the phase of said delayed second digital signal so as to generate the complex conjugate of said delayed second digital signal; digitally multiplying said second digital signal with said complex conjugate of said delayed second digital signal to generate a third digital signal, said third digital signal having a real and an imaginary component;

determining said imaginary component of said third digital signal;

digitally integrating said imaginary component of said third digital signal so as to generate a signal corresponding to said phase changes of said FM digital complex signal.

6. The method as described in Claim 5 wherein said oversampling factor is approximately equal to 18 and said FM digital demodulator determines said phase changes with an associated worst case error factor of less than or equal to -60 dB.

7. A method of determining phase changes in an FM digital complex signal having an associated modulating signal and an associated sampling frequency, said modulating signal having an associated modulating frequency, said FM digital complex signal being highly oversampled wherein said sampling frequency is much greater than said modulating frequency times an oversampling factor N, said method comprising the steps of:

negating the phase of said delayed second digital signal so as to generate the complex conjugate of said delayed second digital signal; digitally multiplying said second digital signal with said complex conjugate of said delayed second digital signal to generate the imaginary component of a third digital signal;

8. The method as described in Claim 7 wherein said oversampling factor is approximately equal to 18 and said FM digital demodulator determines said phase changes with an associated worst case error factor of less than or equal to -60 dB.

9. A method of determining phase changes in an FM digital complex signal having an associated modulating signal and an associated sampling frequency, said modulating signal having an associated modulating frequency, said FM digital complex signal being highly oversampled wherein said sampling frequency is much greater than said modulating frequency times an oversampling factor N, said method comprising the steps of:

determining a first digital signal that represents the change in phase between two successive samples of said FM digital complex signal;

determining a second digital signal that represents the change in phase between two successive samples of said first digital signal, wherein said second signal has an imaginary component;

digitally integrating the imaginary component of said second signal to determine said phase changes in said FM digital complex signal.

10. An FM digital demodulator for determining phase changes in an FM digital complex signal representing a single channel signal, said FM digital complex signal having an associated modulating signal and an associated sampling frequency, said modulating signal having an associated deviation frequency, said single channel signal having a center frequency that is centered about a given non-zero intermediate frequency, said FM digital complex signal being highly oversampled wherein said sampling frequency is much greater than said deviation frequency times an oversampling factor N, said FM digital demodulator comprising:

a means for shifting said center frequency to approximately zero frequency to generate a frequency shifted signal of said FM digital complex signal;

a first means for delaying said frequency shifted signal by one sample delay so as to generate a delayed frequency shifted signal;

a first means for negating the phase of said delayed frequency shifted signal so as to generate a complex conjugate signal of said delayed, frequency shifted signal;

a first means for digitally multiplying said frequency shifted signal with said complex conjugate signal to generate an output signal wherein the imaginary portion of said output signal is equal to said phase changes of said FM digital complex signal.

11. The digital demodulator as described in Claim 10 wherein said associated oversampling factor is equal to 18 and said FM digital demodulator determines said phase changes with an associated worst case error factor of less than or equal to -60 dB.

12. A method for determining phase changes in an FM digital complex signal representing a single channel signal, said FM digital complex signal having an associated modulating signal and an associated sampling frequency, said modulating signal having an associated deviation frequency, said single channel signal having a center frequency that is centered about a given non-zero intermediate frequency, said FM digital complex signal being highly oversampled wherein said sampling frequency is much greater than said deviation frequency times an oversampling factor N, said method comprising the steps of: shifting said center frequency of said FM digital complex signal to approximately zero frequency to generate a frequency shifted signal of said FM digital complex signal;

delaying said frequency shifted signal by one sample delay so as to generate a delayed frequency shifted signal;

negating the phase of said delayed frequency shifted signal so as to generate a complex conjugate signal of said delayed frequency shifted signal; digitally multiplying said frequency shifted signal with said complex conjugate signal to generate an output signal, wherein said imaginary portion of said output signal is equal to said phase changes of said FM digital complex signal.

13. The method described in Claim 12 wherein said associated oversampling factor is equal to 18 and said FM digital demodulator determines said phase changes with an associated worst case error factor of less than or equal to -60 dB.