# Obtain frequency response from digital filter with DSP.jl

**URL:** <https://discourse.julialang.org/t/obtain-frequency-response-from-digital-filter-with-dsp-jl/44618>\
**Category:** Signal and Image Processing\
**Created:** [August 9, 2020, 2:33pm UTC](https://discourse.julialang.org/t/obtain-frequency-response-from-digital-filter-with-dsp-jl/44618 "2020-08-09T14:33:36Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![marcpabst](https://avatars.discourse-cdn.com/v4/letter/m/4bbf92/32.png) [@marcpabst](https://discourse.julialang.org/u/marcpabst)\
**Post date:** [August 9, 2020, 2:33pm UTC](https://discourse.julialang.org/t/obtain-frequency-response-from-digital-filter-with-dsp-jl/44618/1 "2020-08-09T14:33:36Z")

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Hi, I have a simple and potentially very stupid question. I use `DSP.jl` to construct a filter via `digitalfilter()`, which leaves me with a filter kernel I can apply to my signal.

If I wanted to take a look at the response in the frequency domain, `freqz()` seems to be the appropriate function. However, it only accepts filter coefficient objects, which leads to the question of how to convert a filter kernel from `digitalfilter()` to such an object.

I found the documentation of what otherwise looks like an excellent and well-designed package a bit sparse (at least for people with no DSP background), but it seems like this does what I want for filters constrcuted with the `remez()` method:

```julia
julia> bpass = remez(35, [(0, 0.1)=>0, (0.15, 0.4)=>1, (0.45, 0.5)=>0]);
julia> b = DSP.Filters.PolynomialRatio(bpass, [1.0])
julia> f = range(0, stop=0.5, length=1000)
julia> plot(f, 20*log10.(abs.(freqz(b,f,1.0))))

```

It seems to work just fine für filters created by `digitalfilter()`, so am I correct that e.g. `DSP.Filters.PolynomialRatio(digitalfilter(FIRWindow(hamming(3), Highpass(10; fs=100)), [1.0])` will yield a correct frequency response?

And a bonus question: Does anyone have a good resource for learning about how these filter coefficients relate to e.g. a window-based FIR filter?

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<div class="post-metadata">

**Author:** ![rafael.guerra](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rafael.guerra/32/216610_2.png) [@rafael.guerra](https://discourse.julialang.org/u/rafael.guerra)\
**Post date:** [August 23, 2020, 2:55pm UTC](https://discourse.julialang.org/t/obtain-frequency-response-from-digital-filter-with-dsp-jl/44618/2 "2020-08-23T14:55:59Z")

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I am not an expert but some feedback:

- It seem that freqz does not compute the frequency response of FIR filters (it works alright for others).
- You can use function available in: [FIRfreqz](https://github.com/JunoLab/Weave.jl/blob/master/examples/FIR_design_plots.jl), to display your FIR filter response as follows:

```julia
fs = 100
f = digitalfilter(Highpass(10; fs=fs), FIRWindow(hamming(3)))
w = range(0, stop=pi, length=1024)
h = FIRfreqz(f, w)
ws = w/pi*(fs/2)
plot(ws, 20*log10.(abs.(h)), xlabel="Frequency(Hz)",ylabel="Magnitude(db)",label="10Hz high-pass" )

```

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<div class="post-metadata">

**Author:** ![marcpabst](https://avatars.discourse-cdn.com/v4/letter/m/4bbf92/32.png) [@marcpabst](https://discourse.julialang.org/u/marcpabst)\
**Post date:** [August 31, 2020, 5:47pm UTC](https://discourse.julialang.org/t/obtain-frequency-response-from-digital-filter-with-dsp-jl/44618/3 "2020-08-31T17:47:41Z")

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Thanks! That helps actually quite a lot! My understanding is that `sw += b[j]*exp(-im*w[i])^-j` is basically just a Fourier transformation, right?

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<div class="post-metadata">

**Author:** ![rafael.guerra](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rafael.guerra/32/216610_2.png) [@rafael.guerra](https://discourse.julialang.org/u/rafael.guerra)\
**Post date:** [September 1, 2020, 9:50pm UTC](https://discourse.julialang.org/t/obtain-frequency-response-from-digital-filter-with-dsp-jl/44618/4 "2020-09-01T21:50:39Z")

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Correct. Called Discrete Time Fourier Transform (DTFT) in article [FIR\_filter](https://en.wikipedia.org/wiki/Finite_impulse_response), see the FIR filter’s frequency response equation in section “Frequency response”.

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**Author:** ![Adriel](https://avatars.discourse-cdn.com/v4/letter/a/f07891/32.png) [@Adriel](https://discourse.julialang.org/u/Adriel)\
**Post date:** [September 2, 2020, 4:59am UTC](https://discourse.julialang.org/t/obtain-frequency-response-from-digital-filter-with-dsp-jl/44618/5 "2020-09-02T04:59:33Z")

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As a quick hack, you could extend `freqz` to work with FIR filters.

```julia
freqz(h::Vector{T}, N) where T = fft([h; zeros(T, N-length(h))])

```

Edit: In this case the corresponding normalised frequency vector (in radians) would be

```julia
w = range(0, step=2π/N, length=N)

```