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most system have 48khz and if i have 40tap low pass fir filter that cutoff freuqency is 300hz, filter delay is 1/48000*20 = 0.0004s but the frequency resolution is very sparse and i think if the filter have complicated shape the performance is not good.

and if i do downsampling to 2000hz, performance is better if i design filter in that sampling rate. but filter time delay is 1/2000*20 = 0.01s. this delay burden me....

is there method to overcome this problem?

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  • $\begingroup$ I'm doubting the performance of a 40-tap low-pass FIR filter with $f_s=48$ kHz and $f_c=300$ Hz. Why not use an IIR filter? Does linear phase necessary for your application? BTW, if you downsample to 2 kHz, you may design a low-pass filter with a lower order which has less delay. $\endgroup$
    – ZR Han
    Commented Jan 27, 2022 at 6:21
  • $\begingroup$ Thank you ZR Han, what i am actually using is arbitarary shape filter so i have to use FIR filter and the frequency resolution have to be close to have good performance. but problem is if i have 48khz sampling frequency the filter tap is large and if i do downsampling filter tap is small but delay is large...... $\endgroup$
    – gg h
    Commented Jan 27, 2022 at 6:29
  • $\begingroup$ What's your frequency region of interest? If you downsample the signal to 2kHz, the FIR filter (impulse response) should also be downsampled to 2kHz, they should have the same sampling rate. dsp.stackexchange.com/questions/81205/… $\endgroup$
    – ZR Han
    Commented Jan 27, 2022 at 6:38
  • $\begingroup$ I dunno what you mean by "delay". I'm assuming you are talking about group delay because you calculate the delay as a half of the filter length, but I'm not sure since you said that it's an arbitrary shape filter. If you are saying input-output delay, you can implement an FIR filter with only one sample delay. $\endgroup$
    – ZR Han
    Commented Jan 27, 2022 at 6:43
  • $\begingroup$ i make frequency response from equation using frequency sampling method that is arbitrary shape but it's impulse response show non-causal property so i delay half of filter length. $\endgroup$
    – gg h
    Commented Jan 27, 2022 at 6:47

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is there method to overcome this problem?

Sure. The delay is caused by using a linear phase filter. If care about the magnitude response and minimum delay, you should design a minimum phase filter instead. This will eliminate any bulk delay and concentrate the energy in the impulse response as much to the "front" as is possible, i.e.

$$\sum h^2[n] \stackrel{!}{=} \min $$

Minimum phase design is harder than linear phase design, but it can certainly be done for both FIR and IIR filters.

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