Multirate Signal Processing for Communication Systems by Fredric J. Harris

By Fredric J. Harris

This booklet offers the communications engineer all in favour of the actual layer of communications structures, the sign processing innovations and layout instruments had to strengthen effective algorithms for the layout of assorted structures. those sytems inlcude satellite tv for pc modems, cable modems, wire-line modems, cell-phones, a number of radios, multi-channel receivers, audio encoders, surveilance receivers, laboratory tools, and diverse sonar and radar structures. The emphasis woven in the course of the publication fabric is that of intuitive knowing acquired by means of the liberal use of figures and examples. The e-book comprises examples of a majority of these forms of structures. The booklet will also comprise MATLAB script documents that enforce the examples in addition to layout instruments for filters just like the examples.

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2 WINDOWING The problem with the sample set of the prototype filter is that the number of samples is unbounded and the filter is noncausal. If we had a finite number of samples, we could delay the response to make it causal. Our first task then is to form a finite list of filter coefficients from the unbounded set. The process of pruning an infinite sequence to a finite sequence is called windowing. • operator is the standard MATLAB point-by-point multiply. hw (n) = w(n) . 6) The expression for the spectrum of the windowed impulse response is shown in (3.

While the scaling factor is required to cancel tbe processing gain of the filter weights, it should not be applied to tbe coefficient set since it reduces the precision with which the coefficients are represented, which leads to an increase in arithmetic noise of tbe filter process. This is a common source of error in filter design routines, one tbat is easily corrected by scaling the filter coefficients by the maximum weight so that the maximum weight is unity rather than 2f1/f,. 2, which represents a loss in coefficient precision of more than 2 bits.

4). 4) The sequence SM(n-r) is seen to be the sum of M complex sinusoidal sequences with amplitude (1/M), with phase angles exp(-j r m27t/M) at frequencies equally spaced around the unit circle at multiples of (21t/M). 5). 4. I. 4 Sampling Sequence Ss(n-1) in Time and Frequency Domain The resampling operation can be visualized as the product of the input sequence x(u) and the sampling sequence SM(n) to obtain the output sequence x0(Mn). The time domain product causes a frequency domain convolution.

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