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Supposing I have a discrete time signal x(n). when I pass this through an FIR filter h(n), and again pass this result through h(n) again (essentially this is a second order filtering), the group delay increases by a factor of 2. what are the practical implications of this?

The same concept is used while implementing a matched filter receiver . where the same filter which is used in the transmitter side is also used in the receiver side.

Thanks in advance

phani tej

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This is not what a matched filter does. If the pulse shape is \$h(n)\$ then the matched filter's impulse response is \$h(-n)\$ (plus a delay to make it causal). This means that the total phase response is linear (a pure delay). It can be shown that this choice maximizes the SNR at the sampling instant if the noise is white.

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