Multiplying the two waveforms and integrating steps

Digital Communications ENB346

Lecture 2 - 2009

Matched Filter Implementation of the correlator

• Since the correlation operation can be regarded as a filtering operation the correlator can be implemented as a filter.

• Matched filter

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t = kTs

Substituting for the impulse response in the equation for Z(t):

when t = Ts, this can be written as:

See example in the next slide

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matched filter output

Figure shows the correlator and matched filter outputs for a symbol consisting of a sinusoidal burst of duration Ts. Note that the outputs the correlator and the
matched filter are identical at t=Ts. 10

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Matched filter and correlator

Example 4
Determine the impulse response of a matched filter for the following transmitted symbol S(t):

S(t) = A/2 for 0≤t ≤ T/2

Frequency Response of a matched Filter

Given a matched filter with impulse response h(t), its frequency response H(f) is given by

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The frequency domain view of
matched filtering

Matched Filter Example (cont.)

Symbol energy Es is given by

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average symbol energy (assuming all M symbols are equiprobable)

is:

Example 1

Consider a binary communication system that receives equally likely signals S1(t) and S2(t) in AWGN.

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Solution to Example 1

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Effect of shape of the symbol pulse waveform on the correlation receiver

This maximum SNR can be determined and is dependent on the Energy E of the symbol.

The expression for the maximum SNR is given in the next slide (For proof see Text book Sklar)

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Thus we have the important result that the signal-to-noise ratio at the output of the correlator depends only on the ratio of signal energy to the single sided power spectral density of white noise at the filter output and thus is not dependent on the shape of the waveform that is used.

= -A/2 for T/2<t ≤ T

The symbol is transmitted over a channel
with noise power spectral density of

Lecture 1- Self Learning Tutorial (cont.)

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Lecture 1- Self Learning Tutorial (cont.)

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Lecture 1- Self Learning Tutorial (cont.)

Lecture 1- Self Learning Tutorial (cont.)