[SciPy-User] interpolating an impulse response

[henry lindsay smith]

yes I don't care about matching phase.  It's for loudness estimation so I
will be summing the power afterwards

I'll have a go at the fft/ifft method you suggested.

On Tue, Apr 12, 2011 at 5:54 AM, Charles R Harris <charlesr.harris at gmail.com
> wrote:

>
>
> On Mon, Apr 11, 2011 at 10:23 PM, Charles R Harris <
> charlesr.harris at gmail.com> wrote:
>
>>
>>
>> On Mon, Apr 11, 2011 at 11:41 AM, henry lindsay smith <
>> henrylindsaysmith at gmail.com> wrote:
>>
>>> ok, my filter knowledge is a bit rusty it seems.
>>>
>>> I have a simple filter - for a loudness model.  It is specified at
>>> 48khz.  it is a 2nd order IIR filter.  To have the same frequency response
>>> at 44.1khz I think I need to interpolate the impulse response.  however
>>> thats hard when there are only 3 coefficient in a and b.  any ideas?
>>>
>>
>> I don't think you can do it exactly. If you have O[n] + a_0 * O[n-1] + a_1
>> * O[n-2] + ... = I[n], the frequency response of the left hand side is 1 +
>> a_0/z + a_1/z^2 + ..., where z = exp(2*pi*j*f/48e3). Note the discrete set
>> of frequencies. Trying to match a sum of such such discrete frequencies with
>> a sum of differently spaced discrete frequencies isn't going to work, the
>> results will have different fundamental periods. However, presuming that the
>> input has gone through an anti-aliasing filter up front, you should be able
>> to make an approximation over the range of frequencies you are interested in
>> that is probably good enough by resampling in the frequency domain, doing an
>> inverse fft, and discarding the smaller coefficients in the result.
>>
>>
> This changes a bit if you don't care about matching the phase, which I
> suspect is the case here.
>
> Chuck
>
>
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