Partial response schemes: impulse & frequency response

Impulse response and frequency response of PR signaling schemes

Consider a minimum bandwidth system in which the filter is represented as a cascaded combination of a partial response filter and a minimum bandwidth filter . Since is a brick-wall filter, the frequency response of the whole system is equivalent to frequency response of the FIR filter , whose transfer function, for various partial response schemes, was listed in Table 1 in the previous post (shown below).

The hand-crafted Matlab function (given in the book) generates the overall partial response signal for the given transfer function . The function records the impulse response of the filter by sending an impulse through it. These samples are computed at each symbol sampling instants. In order to visualize the pulse shaping functions and to compute the frequency response, the impulse response of are oversampled by a factor . This converts the samples from symbol rate domain to sampling rate domain. The oversampled impulse response of filter is convolved with a sinc filter that satisfies the Nyquist first criterion. This results in the overall response of the equivalent filter (refer Figure 2 in the previous post).

This article is part of the book Wireless Communication Systems in Matlab, ISBN: 978-1720114352 available in ebook (PDF) format (click here) and Paperback (hardcopy) format (click here).

The Matlab code to simulate both the impulse response and the frequency response of various PR signaling schemes, is given next (refer book for the Matlab code). The simulated results are plotted in the following Figure.

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Topics in this chapter

Pulse Shaping, Matched Filtering and Partial Response Signaling ● Introduction ● Nyquist Criterion for zero ISI ● Discrete-time model for a system with pulse shaping and matched filtering  □ Rectangular pulse shaping  □ Sinc pulse shaping  □ Raised-cosine pulse shaping  □ Square-root raised-cosine pulse shaping ● Eye Diagram ● Implementing a Matched Filter system with SRRC filtering  □ Plotting the eye diagram  □ Performance simulation ● Partial Response Signaling Models  □ Impulse response and frequency response of PR signaling schemes ● Precoding  □ Implementing a modulo-M precoder  □ Simulation and results