By Marvin Frerking
An engineer's creation to thoughts, algorithms, and developments in electronic sign Processing. This lucidly written source makes large use of real-world examples because it covers all of the vital layout and engineering references.
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Additional resources for Digital Signal Processing in Communication Systems
16). 43) Convolution can be thought of as summing the output of a system to many infinitesimally short values of the input displaced in time. Thus, the output of the network at time to is obtained by multiplying the input at t = to by the impulse response for t = 0 or h(O)f(to)' This is added to the response of the network to the input function f(to - ~t) multiplied by the impulse response for ~t or f(to - ~t) h(~t). This is added to the response to the input at t - 2~t which, at time to' is given by f(to - 2~t) h(2~t), etc.
32) Digital Signal Processing Concepts 21 Thus, if the frequency spectrum off(t) is illustrated in Fig. 11a, then the spectrum of is illustrated in Fig. 11 b. The proof of this theorem is left as an exercise for the reader (see Problem 2-11). We shall make frequent use of the function f(t) itself. Therefore, it is appropriate to determine its frequency spectrum. 35) The frequency spectrum is shown in Fig. 12. This leads directly to the transforms for sin(2nfot) and cos(2nfot). 37) and, from Eq.
Shown here is the absolute value of the real part ofthe FFT output. Note the symmetry about the center, k = 8. Thus, a value for k = 7 corresponds to a frequency o 4 I 8 INDEX VALUE. 18 Real part ofFFT output for real input signal I 12 16 Digital Signal Processing Concepts 29 (7/l6)FS' while a value k = 9 corresponds to (-7/16)Fs. If the imaginary part of the output were shown, the plot would exhibit odd symmetry about the value k = 8. It should be noted that if the input is real and has even symmetry about the center value n = N/2, the output is purely real while an input function exhibiting odd symmetry about the center value n = NI2 gives a purely imaginary result.