By Andre Quinquis
This publication makes use of MATLAB as a computing instrument to discover conventional DSP issues and remedy difficulties. This vastly expands the variety and complexity of difficulties that scholars can successfully learn in sign processing classes. a good number of labored examples, machine simulations and purposes are supplied, besides theoretical features which are crucial with the intention to achieve a great figuring out of the most subject matters. practising engineers can also locate it valuable as an introductory textual content at the topic.
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12. 15. Magnitude of the Fourier series coefficients Verify the following main properties of the DTFS coefficients corresponding to a periodical real discrete-time signal: c(1) = 1 N N −1 ¦ x [ n + 1] , c( N 2) = n =0 1 N N −1 ¦ x [ n + 1] (−1)n , cN −k = ck∗ n =0 48 Digital Signal Processing using MATLAB Write a new code to calculate the DTFS coefficients of a 2D discrete-time signal. 16. 13. Write a MATLAB function for calculating the DTFT of a discrete-time finite signal h[n] of length N, for N uniformly spaced frequencies on the unit circle.
Use the function rand to generate 1,000 independent values of the random variable X defined by: P ( X = −1) = p 0 ; P( X = 0) = p1 ; P ( X = 1) = 1 − p 0 − p1 ; where p0 and p1 are the probabilities to be entered by the user. 11. Plot in polar coordinates the poles of the filter having the following transfer function: H ( z) = 1 1 + az −1 + bz −2 The values of a and b are entered by the user and the function returns the poles. (use the commands roots and polar). 5. 12. 1024, where φ is a uniformly distributed random variable on [0, 2π] and b(t) is a white Gaussian noise with mean zero and variance one (use rand and randn).
Discrete-time signals and associated frequency spectra Notice that when a discrete-time signal is periodized, its spectrum is sampled. Run the same code again to perform this comparative analysis for the following signals: triangular, sawtooth and exponential. 12. 15. Magnitude of the Fourier series coefficients Verify the following main properties of the DTFS coefficients corresponding to a periodical real discrete-time signal: c(1) = 1 N N −1 ¦ x [ n + 1] , c( N 2) = n =0 1 N N −1 ¦ x [ n + 1] (−1)n , cN −k = ck∗ n =0 48 Digital Signal Processing using MATLAB Write a new code to calculate the DTFS coefficients of a 2D discrete-time signal.