Question

Using shifted impulse response, represent the sequencex(n) = {1,
2,3,1,2}​

Answer 1

Answer:

Colin Campbell, in Surface Acoustic Wave Devices and their Signal Processing Applications, 1989

13.4.1 Correlation and Convolution

A paramount requirement of a spread-spectrum radio communications link is that, within the limits of its design, it should be able to achieve meaningful detection of a digitally encoded message signal, despite its corruption by narrow-band noise in the transmission channel. To achieve this, it must sufficiently increase the signal-to-noise ratio of the signal, and this involves encoding the transmission in such a manner that the spectrum of the transmitted signal is artificially broadened. A reference copy of the coding scheme used for such broadening must then be contained within the receiver for auto- or cross-correlation with the received signal.

To distinguish between convolution and correlation, recall the convolution relation given in eqn (3.9) of Chapter 3 as

(3.9)

for the convolution of two time signals f1(t) and f2(t), where the right-hand expression is a “shorthand” notation for convolution. When applied to the response of a linear filter subjected to an input stimulus f1(t) = s(t), the output response f(t) is given by the convolution of s(t) with the impulse response h(t) of the filter. Substitution of h(t) = f2(t) in eqn (3.9) yields

Explanation:

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