Fully digital spectrum analyzer using time compression and Discrete Fourier Transform techniques
First Claim
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 Xk,p for each of K spectral lines (where k = 1, 2, 3, . . . , K), each power value Xk,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 2b (aYk,p-1 + 2-b Xk,p), where Yk,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 (2b-1 <
p ≦
2b), and (a) is 1/2 if (p-1 = 2b-1) and is 1 otherwise.
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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.
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Citations
10 Claims
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1. A spectrum analyzer comprising:
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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 Xk,p for each of K spectral lines (where k = 1, 2, 3, . . . , K), each power value Xk,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 2b (aYk,p-1 + 2-b Xk,p), where Yk,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 (2b-1 <
p ≦
2b), and (a) is 1/2 if (p-1 = 2b-1) and is 1 otherwise. - View Dependent Claims (2, 3, 4, 5)
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6. A spectrum analysis method comprising the steps of:
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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 Xk,p (where k = 1, 2, 3, . . . , K), each power value Xk,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 2b (aYk,p-1 + 2-b Xk,p), where Xk,p-1 represents the value of the term inside the parenthesis for the p-1 sequence of digital words, (b) is defined as 2b-1 <
p ≦
2b, and (a) is 1/2 if p-1 = 2b-1 and is 1 otherwise, the value of the expression being a sum mode average of said power values. - View Dependent Claims (7)
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8. A spectrum analyzer comprising:
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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. - View Dependent Claims (9)
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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.
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Specification