# digital IIR filter delay and oversampling

Can oversampling decrease the delay of digital IIR filter? Imagine there is some digital signal going into processor that applies low pass filter.Lets say its 1 KHz sample rate and the filter is second order gaussian lowpass with -3db point at 100 Hz.

The putput of this digital filter will be delayed,this delay will vary with frequency.Can this delay,in the band of our interest which is 0 - 500 Hz for 1 KHz sample rate,be decreased if we increase the sample rate of the incoming signal?

What if the incoming signal was 2 KHz samplerate ( 2x oversampling ),would it decrease the digital filter delay?

I have read that the delay can be decreased by increasing bandwidth or by putting -3db cut off point higher in frequency.Is that true? I know making the low pass have higher frequency decrease the delay,but what about the bandwidth?

If we increase the sample rate,we increase the bandwidth,but in case of low pass filter it will be the bandwidth thats being attenuated.I have feeling that the author who wrote about the bandwidth thing meant the passband bandwidth and in that case its same thing as making the low pass higher.

I tried two filter simulating softwares,the Iowa Hills IIR and MicroModeler.com and got conflicting results.The Iowa Hills showed that the delay in the band of interest is increased slightly by oversampling while MicroModeler showed small decrease.

Does oversampling increase,decrease or not change the delay?

Note that a given digital filter impulse response $h[n]$ will have a corresponding equivalent analog frequency response $H(e^{j\omega})$ through the sampling relations; hence with the given sampling rate Fs.

This means that if you change the sampling rate of the input of this filter, then the effective analog filter response will also be changed, probably that's not what you want to have. So you have to redesign the digital filter to recreate the desired analog filter response.

In particular, when you increase the sampling rate by two, then the digital filter $h[n]$ should be redesigned such that its digital frequency response cutoff frequency is halved, so that the associated analog cutoff frequency would remain the same.

That means that, since the digital cutoff frequency is halved, the filter impulse response is doubled in length, the delay is doubled too. But don't worry, as the sampling period is also halved, the associated analog delay remains the same.

Of course, delay here refers to that associated with the decay time of the digital IIR impulse response $h[n]$.

• So both of these filter simulators are wrong since one is showing decrease while other shows increase? If you say that the delay in seconds stays practically the same,then both of these simulators are flawed. – Sweeper Aug 24 '18 at 23:48
• They are referring to slight changes, through pass bands. Do they re-design the filters when you change the sampling rate? – Fat32 Aug 24 '18 at 23:52
• There is no setting to turn automatic re-design on in any of these softwares.I did however re-design them manually each time.For example,if the filter cut off is specified by -3db point with number from 0 to 1 where 1 is nyquist,I set it to 0.1024 for samplerate x1,then manually decreased it to 0.0512 for 2x oversampling,0.0256 for 4x oversampling etc.... maybe its some computational inaccuracy due to insufficient internal resoultion,a quantization error. – Sweeper Aug 25 '18 at 0:16
• ok you do it right. Changing the digital cutoff frequency, equates to redesigning. Of course there are other tolerances such as transition bandwidth which has a huge effect on the impulse response length. Everything being the same however delay remains same. slight changes might be indeed due to quntization issues etc. Yet, more probably, some pass/stop band tolerances might have changed too. – Fat32 Aug 25 '18 at 0:23