Assume we want to filter the audio signal from a digital video disc (DVD) player as shown in Figure P5–3. The filtered audio signal drives, by way of a digital-to-analog (D/A) converter, a speaker. For the audio signal to have acceptable time synchronization with the video signal, video engineers have determined that the time delay of the filter must be no greater than $6 × 10^{−3}$ seconds. If the $f_s$ sample rate of the audio is 48 kHz, what is the maximum number of taps in the FIR filter that will satisfy the time delay restriction? (Assume a linear-phase FIR filter, and zero time delay through the D/A converter.)


  • $\begingroup$ You posted a jpeg image of a multi-part IIR filter problem recently. The problem had a designator of 'Q3', a block diagram of an IIR filter, and mentioned the idea of "120 Hz flicker noise from fluorescent lights contaminating a photodiode signal." ROHAN, I need to find the source of that problem: Did it come from a textbook, college lecture notes, a web site, or just where? If you help me find the origin of that IIR filter problem I will reward you. Don't reply to me here on Sig. Proc. StackExchange, but rather, please send me an e-mail at R_dot_Lyons_@_ieee_dot_org. $\endgroup$ Dec 8 '16 at 9:44

577 taps: Since it is a linear phase filter then the dominant tap for a low pass filter will be in the center (as the filter must be symmetric or asymmetric to be linear phase), which therefore sets the total time delay of the filter: the time delay for a dominant center tap filter is the total filter length / 2 * the sampling rate of the filter.

$$ \frac12 \times (577-1) = (6 \times 10^{-3}) \times 48000 $$

  • $\begingroup$ a 1-tap FIR filter has delay of 0. and the order of an FIR filter is 1 less than the number of taps. $\endgroup$ Dec 7 '16 at 7:08
  • $\begingroup$ Is the formula same for both even and odd length? $\endgroup$
    Dec 7 '16 at 7:26
  • $\begingroup$ Robert- Yes, thank you. Rohan Paul: If it is even and symmetric then the delay would be half way between: for example the delay of a two tap symmetric filter is 1/2 a tap. $\endgroup$ Dec 8 '16 at 4:52
  • $\begingroup$ @robertbristow-johnson alright but $h[n]=\delta[n-9]$ is a single (nonzero) tap FIR filter with delay of 9 samples...? May be you're referrig to Type-I,II,III,IV even/odd symmetric causal linear phase FIR filters... $\endgroup$
    – Fat32
    Apr 6 '17 at 9:07
  • $\begingroup$ @fat32 Yes as soon as any non-zero coefficients are present given it is a linear phase filter it must be symmetric or assymmetric. We could of course delay any linear phase filter by adding zeros but since the OP asked for minimum number of taps that would not apply. $\endgroup$ Apr 6 '17 at 10:51

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