# DSP analog filter problem

This problem is taken from the Textbook 'Digital Signal Processing using MatLab' by Ingle/Proakis.

The below system (in the attached file) acts as an analog filter. The analog signal m(t) is passed through an analog to digital converter and m(k) is the resultant discrete or digital output in the form e^(jw). The discrete signal m(k) in the form e^(jw) is applied to the discrete filter h(k) with an impulse response of h (k) = (0.5) k u (k). This is in essence the transfer function of a LTI system. The transfer function is described. See attached file for full problem description.

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#### Solution Preview

1. The below system acts as an analog filter. The analog signal m(t) is passed through an analog to digital converter and m(k) is the resultant discrete or digital output in the form e(jw). The discrete signal m(k) in the form e(jw) is applied to the discrete filter h(k) with an impulse response of h (k) = (0.5) k u (k). This is in essence the transfer function of a LTI system. The transfer function is described below:

m(k) = ejwkâ†’ â†’x(k) = h(ejw) * ejwk

The resultant discrete signal x(k) in the form of ejwk is then fed into a ...

#### Solution Summary

The DSP analog filter programs are examined. The transfer functions of the LTI systems are determined.