FFT, PSD and Windowing functions

[Yared Melese]

Hello

Would you please let me know the package available to do windowing, FFT and PSD?

Currently, I have bin file that I have processed in Julia and need to window it and take preferably PSD but FFT work as well

Thanks

Yared

 

[Islam Badreldin]

Hello Yared,

Take a look at the DSP package

https://github.com/JuliaDSP/DSP.jl

  -Islam

_____________________________
From: Yared Melese <yam0...@gmail.com>
Sent: Wednesday, July 20, 2016 10:15 AM
Subject: [julia-users] FFT, PSD and Windowing functions
To: julia-users <julia...@googlegroups.com>

[Yared Melese]

Hi Islam,

Thanks for your input

 I was able to find all windowing functions; however, there is nothing about PSD ( power spectral density). In python and matlab, there is function pwelch which does both windowing and FFT and wondering if there is the same function in Julia.

Here is simple trial I had but it is complaining about type mismatch

fb= fb[:]*hamming(length(fb))
fb = fft(fb)         # take FFT of signal

LoadError: MethodError: `*` has no method matching *(::Array{Complex{Float64},1}, ::Array{Float64,1})

Closest candidates are:

  *(::Any, ::Any, !Matched::Any, !Matched::Any...)

  *{T<:Union{Complex{Float32},Complex{Float64},Float32,Float64},S}(!Matched::Union{DenseArray{T<:Union{Complex{Float32},Complex{Float64},Float32,Float64},2},SubArray{T<:Union{Complex{Float32},Complex{Float64},Float32,Float64},2,A<:DenseArray{T,N},I<:Tuple{Vararg{Union{Colon,Int64,Range{Int64}}}},LD}}, ::Union{DenseArray{S,1},SubArray{S,1,A<:DenseArray{T,N},I<:Tuple{Vararg{Union{Colon,Int64,Range{Int64}}}},LD}})

  *{TA,TB}(!Matched::Base.LinAlg.AbstractTriangular{TA,S<:AbstractArray{T,2}}, ::Union{DenseArray{TB,1},DenseArray{TB,2},SubArray{TB,1,A<:DenseArray{T,N},I<:Tuple{Vararg{Union{Colon,Int64,Range{Int64}}}},LD},SubArray{TB,2,A<:DenseArray{T,N},I<:Tuple{Vararg{Union{Colon,Int64,Range{Int64}}}},LD}})

  ...

in include_string at loading.jl:282

in include_string at C:\Users\melese\.julia\v0.4\CodeTools\src\eval.jl:32

in anonymous at C:\Users\melese\.julia\v0.4\Atom\src\eval.jl:84

in withpath at C:\Users\melese\.julia\v0.4\Requires\src\require.jl:37

in withpath at C:\Users\melese\.julia\v0.4\Atom\src\eval.jl:53

[inlined code] from C:\Users\melese\.julia\v0.4\Atom\src\eval.jl:83

in anonymous at task.jl:58

while loading D:\userdata\melese\Desktop\fft.jl, in expression starting on line 23

[Islam Badreldin]

Hi Yared,

Please see below,,

On Thursday, July 21, 2016 at 11:19:44 AM UTC-4, Yared Melese wrote:

Hi Islam,

Thanks for your input

 I was able to find all windowing functions; however, there is nothing about PSD ( power spectral density). In python and matlab, there is function pwelch which does both windowing and FFT and wondering if there is the same function in Julia.

Did you take a look at `welch_pgram` function?

http://dspjl.readthedocs.io/en/latest/periodograms.html#welch_pgram 

Here is simple trial I had but it is complaining about type mismatch

fb= fb[:]*hamming(length(fb))
fb = fft(fb)         # take FFT of signal

LoadError: MethodError: `*` has no method matching *(::Array{Complex{Float64},1}, ::Array{Float64,1})

Closest candidates are:

  *(::Any, ::Any, !Matched::Any, !Matched::Any...)

  *{T<:Union{Complex{Float32},Complex{Float64},Float32,Float64},S}(!Matched::Union{DenseArray{T<:Union{Complex{Float32},Complex{Float64},Float32,Float64},2},SubArray{T<:Union{Complex{Float32},Complex{Float64},Float32,Float64},2,A<:DenseArray{T,N},I<:Tuple{Vararg{Union{Colon,Int64,Range{Int64}}}},LD}}, ::Union{DenseArray{S,1},SubArray{S,1,A<:DenseArray{T,N},I<:Tuple{Vararg{Union{Colon,Int64,Range{Int64}}}},LD}})

  *{TA,TB}(!Matched::Base.LinAlg.AbstractTriangular{TA,S<:AbstractArray{T,2}}, ::Union{DenseArray{TB,1},DenseArray{TB,2},SubArray{TB,1,A<:DenseArray{T,N},I<:Tuple{Vararg{Union{Colon,Int64,Range{Int64}}}},LD},SubArray{TB,2,A<:DenseArray{T,N},I<:Tuple{Vararg{Union{Colon,Int64,Range{Int64}}}},LD}})

  ...

in include_string at loading.jl:282

in include_string at C:\Users\melese\.julia\v0.4\CodeTools\src\eval.jl:32

in anonymous at C:\Users\melese\.julia\v0.4\Atom\src\eval.jl:84

in withpath at C:\Users\melese\.julia\v0.4\Requires\src\require.jl:37

in withpath at C:\Users\melese\.julia\v0.4\Atom\src\eval.jl:53

[inlined code] from C:\Users\melese\.julia\v0.4\Atom\src\eval.jl:83

in anonymous at task.jl:58

while loading D:\userdata\melese\Desktop\fft.jl, in expression starting on line 23

This particular error seems to be occurring at the `fb= fb[:]*hamming(length(fb))` line. It looks like you are multiplying an _vector_ of complex doubles with a _vector_ of doubles, which is not mathematically defined because of the dimension mismatch, since both vectors are of dimension Nx1. Instead, my guess is that you meant element-wise multiplication using `.*`. But again, I think the `welch_pgram` function should meet your needs.

  -Islam

[Yared Melese]

Hi Islam,

Thanks again for your inputs,

the first method worked, as  you mentioned it was missing dot to do element wise multiplication.

Here is what it looks like

pow_fs = (((2^(adc_bits-1))-1))^2 / 2
fb= fb.*hanning(length(fb))

When I tried the weltch function, it actually has two sets of data as shown below, how do you split data to plot and manipulate the array?

Here is the command I used,      periodogram(fb; onesided=eltype(fb)<:Real, nfft=nextfastfft(length(fb), fs=150, window=hanning)¶

data collected

 Thanks

Yared

[Islam Badreldin]

Hi Yared,

On Tuesday, July 26, 2016 at 10:25:45 AM UTC-4, Yared Melese wrote:

Hi Islam,

Thanks again for your inputs,

the first method worked, as  you mentioned it was missing dot to do element wise multiplication.

Here is what it looks like

pow_fs = (((2^(adc_bits-1))-1))^2 / 2
fb= fb.*hanning(length(fb))

When I tried the weltch function, it actually has two sets of data as shown below, how do you split data to plot and manipulate the array?

Here is the command I used,      periodogram(fb; onesided=eltype(fb)<:Real, nfft=nextfastfft(length(fb), fs=150, window=hanning)¶

data collected

First, note that you don't have to supply all the keyword arguments if the default values work for you. For example, you can get the same result as above by using

pdg = periodogram(fb; fs=150, window=hanning)

Second, you can split the data by inspecting the field names of the returned result

> fieldnames(pdg)
2-element Array{Symbol,1}:
 :power
 :freq

> fb_power = pdg.power
> fb_freq = pdg.freq

You can then plot this data, using PyPlot for example

using PyPlot
plot(pdg.freq, pdg.power)

I hope this helps.

  -Islam