Spectrum analyzer using delta modulation encoding

• US 3,903,401 A
• Filed: 06/27/1974
• Issued: 09/02/1975
• Est. Priority Date: 06/27/1974
• Status: Expired due to Term

• Current Assignee: Nuggehally Sampath Jayant
• Original Assignee: Nuggehally Sampath Jayant
• Inventors: Jayant, Nuggehally Sampath
• Primary Examiner(s): Atkinson, Charles E.
• Assistant Examiner(s): Smith, Jerry
• Application Number:
  US05/483,899
• Time in Patent Office: 432 Days
• Field of Search: 235/151.3,151.31,156 325/38B 332/11D 324/77R,77B
• US Class Current: 702/76
• CPC Class Codes: G01R 23/16 Spectrum analysis; Fourier analysis

Abstract

Disclosed are a method and apparatus for computing the power spectrum of an applied analog signal at a chosen frequency, by converting the analog signal into a binary sequence, by separately multiplying the binary sequence by a sequence of cosine and sine functions, by accumulating and squaring the resultant product signals, by adding the squared signals, and by multiplying the added signals with a constant signal which is a function of the chosen frequency.

Claims

1. Apparatus for developing a signal representative of the power at a preselected frequency of a predtermined time segment of a delta modulated signal comprising:

first means for multiplying said delta modulated signal with a cosine signal having its argument dependent on said preselected frequency;

second means for multiplying said delta modulated signal with a sine signal having its argument identical to that of said cosine signal;

third means for accumulating said first means output signal;

sixth means for squaring said third means output signal;

fourth means for accumulating said second means output signal;

seventh means for squaring said fourth means output signal; and

fifth means for adding the output signals of said sixth and seventh means.

2. The apparatus of claim 1, further comprising:

a multiplier for multiplying the output signal of said fifth means with a constant signal of a magnitude that is a function of said preselected frequency.

3. Apparatus for developing a signal representative of the power at a preselected frequency of a predetermined time segment of a delta modulated signal comprising:

first means for multiplying said delta modulated signal with a trigonometric function comprising a difference of cosine signals having arguments dependent on said preselected frequency;

second means for multiplying said delta modulated signal with a trigonometric function comprising a difference of sine signals having arguments identical to those of said cosine signals;

third means for accumulating said first means output signal;

fourth means for accumulating said second means output signal;

fifth means for squaring said third means output signal;

sixth means for squaring said fourth means output signal; and

seventh means for adding the output signals of said first and sixth means.

4. Apparatus for developing a signal representative of the power at a preselected frequency of a predetermined time segment of a delta modulated signal comprising:

first means, for generating a difference of cosine signals having arguments dependent on said preselected frequency;

second means, for generating a difference of sine signals having arguments identical to those of said cosine signals;

third means for developing a first product signal of said delta modulated signal with said first means output signal;

fourth means for developing a second product signal of said delta modulated signal with said second means output signal;

fifth means for accumulating said first product signal;

sixth means for accumulating said second product signal;

seventh means for squaring the output signal of said fifth means;

eighth means for squaring the output signal of said sixth means; and

ninth means for adding the output signals of said seventh and eighth means.

5. The apparatus of claim 4, further comprising a multiplier for multiplying the output signal of said means for adding with a constant signal of a magnitude that is a function of said preselected frequency.

6. Apparatus for developing a signal representative of the power at a preselected frequency of a preselected time segment of an applied signal comprising:

a linear delta modulator responsive to said applied signal for generating a binary delta modulated signal;

first means, for generating a difference of cosine signals having arguments dependent on said preselected frequency;

second means, for generating a difference of sine signals having arguments identical to those of said cosine signals;

a first multiplier for multiplying said delta modulated signals with said first means output signal;

a second multiplier for multiplying said delta modulated signal with said second means output signal;

a first accumulator for accumulating the output signal of said first multiplier;

a second accumulator for accumulating the output signal of said second multiplier;

third means for squaring the output signal of said first accumulator;

fourth means for squaring the output signal of said second accumulator;

fifth means for adding the output signals of said third and four means; and

a multiplier for multiplying the output signal of said fifth means for adding with a constant signal having a magnitude that is a function of said frequency.

7. The apparatus of claim 1 wherein said linear delta modulator'"'"''"'"'s binary output signal alternates between +1 and -1.

8. Apparatus for developing a signal representative of the power at a selected frequency, f, of a predetermined time segment of an applied signal comprising:

a linear delta modulator of input step size Delta , responsive to an NT seconds segment of an applied signal and to a clock signal having a period T, developing a binary signal br having values +1 and -1, where r indicates the time position of br and ranges from 1 to N;

a cosine generator providing a signal

9. A spectrum analyzer tuned to a frequency f and responsive to an applied input signal of duration M seconds comprising:

first means responsive to said applied input signal and to a clock signal having a period T seconds for developing a binary signal alternating between +1 and -1 where the integral of said binary signal forms a stepwise approximation of said applied input signal divided by a constant Delta ;

means for generating first trigonometric signals

10. The method of generating a power spectral estimate of an incoming signal at a preselected frequency comprising the steps of:

converting a time segment of said incoming signal in accordance with linear delta modulation techniques into a sequence of N binary signals, br, having values + or - 1 at a rate of 1/T Hz, where r is a variable incrementing from 1 to N;

multiplying each of said binary signals by a difference of cosine signals whose arguments are dependent on said preselected frequency and on said r variable to develop a sequence of N first signals;

multiplying each of said binary signals by a difference of sine signals whose arguments are identical to those of said cosine signals to develop a sequence of N second signals;

accumulating said sequence of N first signals;

accumulating said sequence of N second signals;

independently squaring the resultant signals of said two accumulating steps;

adding said squared signals; and

multiplying said added signals with a constant signal having a magnitude that is a function of said preselected frequency.