Fully digital spectrum analyzer using time compression and Discrete Fourier Transform techniques

• US 3,984,669 A
• Filed: 12/20/1974
• Issued: 10/05/1976
• Est. Priority Date: 05/14/1973
• Status: Expired due to Term

• Current Assignee: Weston Instruments, Inc. (SLB)
• Original Assignee: Weston Instruments, Inc. (SLB)
• Inventors: Lynch, Frank, Lehmann, Joseph L.
• Primary Examiner(s): Malzahn, David H.
• Application Number:
  US05/535,129
• Time in Patent Office: 655 Days
• Field of Search: 235/156, 235/152, 324/77 B, 324/77 D, 179/15 BC
• US Class Current: 708/405
• CPC Class Codes: G01R 23/00 Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
• CPC Class Codes: G01R 23/167 with digital filters
• CPC Class Codes: G06F 17/141 Discrete Fourier transforms

Abstract

A fully digital spectrum analyzer accepting as an input either an analog signal or a series of digital numbers and using time compression and DFT (Discrete Fourier Transform) techniques to provide the spectral component values of the input signal. Novel techniques and means are used in obtaining the power values for selected spectral lines and in averaging these power values. Statistically controlled noise is added to the input of the spectrum analyzer to enhance its resolution beyond the resolution which would be otherwise available. Advanced and efficient techniques are used for generating and applying trigonometric functions in the course of finding the real and imaginary part of Fourier transforms, and for providing running averages of the power spectra.

Claims

1. A spectrum analyzer comprising:

means for generating P successive sequences of digital words (where p = 1, 2, . . . , P), each sequence p representing the time history of an analog signal over a selected time interval;

means for receiving said P sequences of digital words from the generating means and for forming a set of P power values X_k,p for each of K spectral lines (where k = 1, 2, 3, . . . , K), each power value X_k,p representing the power spectrum of the k-th spectral line for the p-th sequence of digital words; and

means for receiving said K.sup.. P power values from the forming means and for averaging the P power values of each of the K spectral lines, comprising means for providing averaging signals representing the expression p^-1 2^b (aY_k,p_-1 + 2^-b X_k,p), where Y_k,p_-1 represents the value of the term inside the parenthesis for the (p-1) sequence of digital words, (b) is defined by the relationship (2^b-1 <

p ≦

2^b), and (a) is 1/2 if (p-1 = 2^b-1) and is 1 otherwise.

2. A spectrum analyzer as in claim 1 wherein the means for providing signals representing said expression comprises p-counter means responsive to the generation of each sequence of digital words from the generating means to provide an output signal representing the current value of (p), b-calculator means for receiving the output of the p-counter counter means and for providing an output signal representing the current value of (b), a-calculator means for receiving the outputs of the p-counter means and the b-calculator means and for providing an output signal representing the current value of (a), (2^-b) calculator means for receiving the output of the b-calculator means and for providing an output representing (2^-b), first multiplier means receiving as inputs the sequences of digital words from the generating means and the output of the 2^-b -calculator means and for providing an output which is the product of its inputs, means for providing the value of said term inside the parenthesis of said expression, second multiplier means for receiving as inputs the last recited term and the output of the a-calculator means and for providing at its output the product of its inputs, summing means for receiving as its inputs the outputs of the first and the second multiplier means and for providing at its output the sum of its inputs, correction factor generator means for receiving as inputs the outputs of the p-counter means and of the b-calculator means and for providing at its output a signal representing ther term (p^-1 2^b), and third multiplier means for receiving as inputs the outputs of the summing means and of the correction factor generator means and for providing an output which is the product of its input, the last recited output being an averaging signal representing said expression for the value of (p) provided by the p-counter means.

3. A spectrum analyzer as in claim 2 wherein the inputs to the first and second multiplier means are represented in binary code and wherein each of the first and second multiplier means comprise a shift register carrying out multiplication by selective shifts of its contents toward the least significant bit.

4. A spectrum analyzer as in claim 1 wherein the generating means include means for generating, after the generation of said P sequences, Q additional sequences of digital words (q = 1, 2, . . . , Q) representing the time history of the analog signal over a selected time interval, the forming means include means for receiving said Q sequences and for forming Q power values X_k,q for each of the K spectral lines, and including exponential mode averaging means for receiving the signal representing the recited expression at p = P, the value of P and the power values X_k,q and for providing, at the q-th sequence of digital words, an output signal representing the expression Y_k,q_-1 + 2^-c (X_k,q - Y_k,q_-1), where Y_k,q_-1 is the value of the term in the parenthesis for the k-th spectral line and the q-1 sequence of digital words, and c = log₂ P.

5. A spectrum analyzer as in claim 4 wherein the exponential mode averaging means comprise:

memory means for storing signals representing the term Y_k,q_-1 and for providing corresponding output signals;

substract means for receiving as inputs the output of the last recited memory means and the K .sup.. Q sequences of power values X_k,q and for providing an output representing the difference between its inputs;

means for generating an output signal representing the term 2^-c ;

multiply means receiving as inputs the outputs of the 2^-c generating means and of the substract means and for providing an output signal representing the product of its inputs; and

sum means for receiving as inputs the outputs of the last recited memory means and the last recited multiply means and for providing an output signal representing the sum of its inputs, said last recited sum being the value of the last recited expression.

6. A spectrum analysis method comprising the steps of:

generating P successive sequences of digital words (where p = 1, 2, . . . , P), each sequence p representing the time history of an analog signal over a selected time interval,

generating a set of power values X_k,p (where k = 1, 2, 3, . . . , K), each power value X_k,p representing the power spectrum of a spectral line k for the p-th sequence of digital words; and

averaging the P power values of each of the K spectral lines to provide signals representing the expression p^-1 2^b (aY_k,p_-1 + 2^-b X_k,p), where X_k,p_-1 represents the value of the term inside the parenthesis for the p-1 sequence of digital words, (b) is defined as 2^b-1 <

p ≦

2^b, and (a) is 1/2 if p-1 = 2^b-1 and is 1 otherwise, the value of the expression being a sum mode average of said power values.

7. A method as in claim 6 including the additional steps of:

generating Q additional sequences of digital words (where q = 1, 2, . . . , Q) and corresponding power values X_k,q ;

receiving the signal representing the recited expression at p = P;

providing at the q-th sequence of digital words an output signal representing the expression Y_k,q_-1 + 2^-c (X_k,q - Y_k,q_-1), where Y_k,q_-1 is the value of the term in the parenthesis of the last recited expression for the k-th spectral line and the q-1 sequence of digital words and c = log₂ P, the last recited output signal representing an exponential mode average of the power values.

8. A spectrum analyzer comprising:

means for deriving a sequence of digital words representing the time history of an analog signal over a selected time interval;

first and second multiplexer means each having a plurality of inputs and an output;

first memory means for storing said digital words and means for applying the contents of said first memory means to a first input of the first multiplexer means;

second memory means and means for applying its contents to a second input of the first multiplexer means;

means storing the values of a single trigonometric function for one quadrant thereof and means for generating therefrom two selected trigonometric functions in selected correspondence to each digital word from the first memory means applied to said first multiplexer means and means for applying said functions to a first input of the second multiplexer means;

first multiplier means having two inputs and an output providing the product of its inputs;

first and second register means;

arithmetic-logic unit means (ALU) having a first and a second input and an output providing a signal which is a defined arithmetic or logic function of its inputs; and

control means including means for causing the first multiplexer means to connect its first input to its output and for causing the second multiplexer means to connect its first input to its output;

means for connecting the outputs of the first and the second multiplexer means to the inputs of the first multiplier means to cause the first multiplier means to provide at its output the product of selected digital words and values of said trigonometric function;

means for alternately storing the output of the first multiplier means in the first and second register means;

means for applying the contents of the first and second register means to the inputs of the ALU means to provide a defined function thereof at the output of the ALU means; and

means for storing the output of the ALU means in the second memory means and means for processing the contents of the second memory means to derive a succession of power values representing the power spectrum of said analog signal.

9. A spectrum analyzer as in claim 8 including means for generating a special window function applied to the second multiplexer means, and wherein the control means includes means, operative prior to the connection of the first inputs of the multiplexer means to the outputs thereof by the control means, for causing the first multiplexer means to connect only its second input to its output and for causing the second multiplexer means to connect only its second input to its output and means for combining the outputs of the multiplexer means in accordance with a selected function.

10. A spectrum analyzer comprising

memory means for storing a set of digital words f(n) representing the time history of an analog signal over a selected time interval;

Dft memory means for storing a corresponding set of intermediate results;

trigonometric memory means for storing the values of a single trigonometric function for only one quardrant thereof;

first, second and third multiplexer means having a number of inputs and a single output that can be connected to a single selected input only;

an R register and an I register, window function storing means and arithmetic means having inputs and an output and providing selected arithmetic and logic functions of its inputs and its output;

means for initially applying the words from the f(n) memory and the window function from the window function storing means to selected inputs of different ones of said multiplexer means, means for concurrently connecting the outputs of the last recited multiplexer means to the last recited inputs thereof, means for applying the last recited multiplexer means outputs to the inputs of the arithmetic means and for causing the arithmetic means to provide at its output a selected function of its inputs, and means for storing the last recited output of the arithmetic means in the DFT memory means;

means for subsequently applying the contents of theh DFT memory means and the contents of the trigonometric memory means in selected relative synchronism for each of K spectral lines (k = 1, 2, . . . , K) to selecting inputs of different ones of said multiplexer means, means for concurrently connecting the outputs of the last recited multiplexer means to the last recited inputs thereof, means for applying the last recited multiplexer means outputs to the inputs of the arithmetic means and for causing the arithmetic means to provide at its ouput a selected function of its inputs, and means for storing the output of the arithmetic means in the R or the I register depending on the trigonometric function concurrently provided from the trigonometric memory means, the storage in the R and I registers being cumulative; and

means for subsequently applying the contents of the R and I registers, for each of said K spectral lines, to selected inputs of different ones of said multiplexer means, means for connecting the outputs of the last recited multiplexer means to the last recited inputs thereof, means for connecting the last recited outputs of the multiplexer means to the inputs of the arithmetic means and for causing the arithmetic means to provide at its output the sum of the squares of the contents of the R and I registers, said sum being representative of the power spectrum value of the corresponding spectral line.