Engee documentation

spectralCrest

Spectral crest for signals and spectrograms.

Library

EngeeDSP

Syntax

Function call

  • crest,spectralPeak,spectralMean = spectralCrest(x,f) — returns the spectral crest of the signal x over time, the peak of the spectrum and the spectral mean. Interpretation x the function depends on the form f.

  • spectralCrest(___,out=:plot) — plots the spectral ridge.

    • If the input signal is in the time domain, the spectral crest graph is plotted as a function of time.

    • If the input signal is in the frequency domain, the spectral crest graph is plotted depending on the frame number.

Arguments

Input arguments

# x — input signal

+ column vector | the matrix

Details

An input signal specified as a vector or matrix. Interpretation x the function depends on the form f.

Типы данных

Float32, Float64

# f is the sampling frequency or frequency vector (Hz)

+ scalar | vector

Details

The sampling frequency or frequency vector in Hz, specified as a scalar or vector, respectively. Interpretation x the function depends on the form f:

  • If f — scalar, x it is interpreted as a signal in the time domain, and f — as a sampling rate. In this case x must be a real vector or a matrix. If x set as a matrix, the columns are interpreted as separate channels.

  • If f — vector, x it is interpreted as a signal in the frequency domain, and f — how are the frequencies in Hz corresponding to the strings x. In this case x must be a real array of size , where — the number of spectral values at the specified frequencies f, — the number of individual spectra, and — the number of channels.

  • Number of lines x, , must be equal to the number of elements f.

Типы данных

Float32, Float64

Name-value input arguments

Specify optional argument pairs as Name,Value, where Name — the name of the argument, and Value — the appropriate value. Name-value arguments should be placed after other arguments, but the order of the pairs does not matter.

Use commas to separate the name and value, and Name put it in quotation marks.

The following name-value arguments apply if x — a signal in the time domain. If x — the signal is in the frequency domain, arguments like "name-value" are ignored.

# Window — the window used in the time domain

+ rectwin(round(f*0.03)) (by default) | vector

Details

The window used in the time domain, defined as a real vector. The number of vector elements must be in the range [1,size(x,1)]. The number of vector elements must also be greater. OverlapLength.

Типы данных

Float32, Float64

# OverlapLength — the number of samples overlapping between adjacent windows

+ round(f*0.02) (by default) | a non-negative scalar

Details

The number of samples overlapping between adjacent windows, set as an integer in the range [0,size(Window,1)).

Типы данных

Float32, Float64

# FFTLength — the number of elements in the DFT

+ numel(Window) (by default) | a positive integer scalar

Details

The number of elements used to calculate the DFT of window input samples, set as a positive integer scalar. If no argument is given, FFTLength by default, it is equal to the number of elements in Window.

Типы данных

Float32, Float64

# Range — frequency range (Hz)

+ [0,f/2] (by default) | A two-element vector is a string

Details

The frequency range in Hz, defined as a two-element vector, is a string of increasing real values in the range [0,f/2].

Типы данных

Float32, Float64

# SpectrumType — spectrum type

+ "power" (by default) | "magnitude"

Details

The type of spectrum specified as "power" or "magnitude":

  • "power" — the spectral crest is calculated for a one-sided power spectrum;

  • "magnitude" — the spectral crest is calculated for a one-sided amplitude spectrum.

Типы данных

String

# out — type of output data

+ :data (by default) | :plot

Details

Type of output data:

  • :data — the function returns data;

  • :plot — the function returns a graph.

Output arguments

# crest — spectral crest

+ scalar | vector | the matrix

Details

A spectral ridge returned as a scalar, vector, or matrix. Each line crest corresponds to the spectral ridge of the window x. Each column crest corresponds to an independent channel.

# spectralPeak — peak of the spectrum

+ scalar | vector | the matrix

Details

The peak of the spectrum returned as a scalar, vector, or matrix. Each line spectralPeak corresponds to the spectral ridge of the window x. Each column spectralPeak corresponds to an independent channel.

# spectralMean — spectral mean

+ scalar | vector | the matrix

Details

The spectral average returned as a scalar, vector, or matrix. Each line spectralMean corresponds to the spectral ridge of the window x. Each column spectralMean corresponds to an independent channel.

Examples

Spectral crest of the signal in the time domain

Details

Let’s create an FM signal with white Gaussian noise and calculate the crest using the default parameters.

import EngeeDSP.Functions: chirp, randn, spectralCrest

fs = 1000
t = (0:1/fs:10)
f1 = 300
f2 = 400
x = chirp(t, f1, 10, f2) + randn(length(t), 1)

crest = spectralCrest(x, fs)

Let’s plot the dependence of the spectral ridge on time.

spectralCrest(x, fs, out=:plot)

spectralCrest 1

([4.987046327015055, 5.236871947723927, 7.544804457899835, 10.3772996669661, 7.705619466415934, 5.99985432220379, 4.868975479415114, 5.902444766668258, 5.6781203280701815, 6.523480840096338  …  7.803614225515488, 8.289150599849984, 8.382547366360493, 6.028262627692971, 6.683863065009292, 5.194224063455523, 3.7499682104979466, 5.218718311184415, 3.207068721139457, 6.082745967003252], [0.439680011925611, 0.601102975643176, 1.034484757673182, 1.3330997948299792, 0.8496287200130014, 0.4947671774843161, 0.43476209921716236, 0.5070692566692776, 0.6240111902833801, 0.8937070726200211  …  0.962580947281854, 1.2053879463201618, 1.4011032035761652, 0.8161989525511318, 0.716299380591645, 0.37571979028258434, 0.25389759893331165, 0.48721486174074174, 0.31362312100811496, 0.6811440879165471], [0.08816441298005284, 0.11478282868925793, 0.13711220263502233, 0.12846307205270513, 0.11026092369549412, 0.08246319842355515, 0.08929231643396737, 0.08590834420556587, 0.1098974932247451, 0.1369984973554123  …  0.1233506577163312, 0.14541754692476894, 0.16714527724577494, 0.1353953871886124, 0.10716847033290458, 0.072334151490691, 0.06770660034464596, 0.09335910326805238, 0.09779120694884458, 0.11197970318200254], Plot{Plots.PlotlyJSBackend() n=1})

Spectral crest of the signal in the frequency domain

Details

Let’s create an LFM signal with white Gaussian noise, and then calculate the spectrogram using the function stft.

import EngeeDSP.Functions: chirp, randn, stft

fs = 1000
t = (0:1/fs:10)'
f1 = 300
f2 = 400
x = chirp(t, f1, 10, f2) + randn(size(t)...)

s, f = stft(x, fs, "FrequencyRange", "onesided")
s = abs.(s).^2

Calculate the crest of the spectrogram over time.

import EngeeDSP.Functions: spectralCrest

crest = spectralCrest(s, f)

Let’s plot the dependence of the spectral ridge on the frame number.

spectralCrest(s, f, out=:plot)

spectralCrest 2

([13.278262719339581, 11.423943909400123, 10.704344652278133, 7.265409265608759, 15.671348771900583, 17.14664360019774, 16.805060471491807, 14.696328543184194, 17.09013028905847, 15.936360071580983  …  16.710312667671143, 16.761812477538534, 12.62023888820894, 10.886155724606253, 13.208164879678929, 15.219986950457587, 11.520098623729307, 16.272350151097733, 18.269299846830197, 16.45774860128549], [1038.875221526367, 1003.8420042054646, 878.9222908403066, 340.3639889446644, 1013.9709212810934, 1511.5917119138305, 1166.5576026614406, 845.4456363019548, 1122.2172446705913, 1132.3238949123497  …  1483.6967321132968, 1213.326351390993, 859.9980861071526, 864.0666804644605, 1179.3520050171578, 766.8614058144813, 652.278982569946, 1323.7297764621535, 1825.3095783670533, 1640.464109040237], [78.23879098379803, 87.87175533831703, 82.10893047555709, 46.847187336823175, 64.70221140755848, 88.15671143339087, 69.41704283899455, 57.52767664506604, 65.66463951354794, 71.05285584828131  …  88.78928609060397, 72.38634563039626, 68.14435873402103, 79.37298549858043, 89.28961863821208, 50.38515527711577, 56.62095472224257, 81.34840783111189, 99.91130441070254, 99.67730998832384], Plot{Plots.PlotlyJSBackend() n=1})

Specifying parameters other than the standard ones

Details

Let’s create an FM signal with white Gaussian noise.

import EngeeDSP.Functions: chirp, randn

fs = 1000
t = (0:1/fs:10)
f1 = 300
f2 = 400
x = chirp(t, f1, 10, f2) + randn(length(t), 1)

Calculate the peak of the power spectrum over time. Calculate the peak for Hamming windows with a duration of 50 ms with overlap 25 ms. We use the range from 62.5 Hz to fs/2 to calculate the peak.

import EngeeDSP.Functions: spectralCrest, hamming

crest = spectralCrest(x, fs,
                      "Window", hamming(round(Int, 0.05*fs)),
                      "OverlapLength", round(Int, 0.025*fs),
                      "Range", [62.5, fs/2])

Let’s plot the dependence of the ridge on time.

spectralCrest(x, fs,
              "Window", hamming(round(Int, 0.05*fs)),
              "OverlapLength", round(Int, 0.025*fs),
              "Range", [62.5, fs/2],
              out=:plot)

spectralCrest 3

([9.538007545680625, 5.730876827698805, 5.032509222116753, 8.153962933846854, 6.409421405881727, 5.675496154818911, 3.936388047909756, 6.4173265830507695, 8.571412474805326, 8.245914575869225  …  9.01887114861341, 6.801343613682713, 4.948170085776451, 4.303209591503631, 6.032361588552264, 5.892015558392096, 4.323588797979937, 4.386216853001777, 5.755291814282484, 8.589943998230682], [1.072192257755449, 0.7611738870970485, 0.6151487100923281, 0.694504549763681, 0.41087548375427874, 0.35978967731876343, 0.38720592502049855, 0.3867047677182591, 0.846628743616088, 0.5501511870614189  …  0.9982941134388452, 0.6086401775262335, 0.16918248208293274, 0.2568272244259427, 0.4861993272274322, 0.563021155034732, 0.48023412546096145, 0.37966201056426135, 0.5141970164720814, 1.0541601271133798], [0.11241260322141401, 0.1328197952917255, 0.12223498913601331, 0.08517386642522173, 0.06410492581705285, 0.06339351970369599, 0.0983657912552872, 0.06025948075318637, 0.09877353891259522, 0.06671803133534474  …  0.11068947510047597, 0.08948822645892963, 0.03419091889530009, 0.0596827133247307, 0.08059850526037807, 0.09555663074120903, 0.11107303397708311, 0.08655796630402203, 0.08934334401533499, 0.12272025607274167], Plot{Plots.PlotlyJSBackend() n=1})

Algorithms

The spectral crest is calculated as described in [1]:

where

  • — spectral value in bin ;

  • and — band boundaries in bins, which are used to calculate the spectral crest.

Literature

  1. Peeters, G. «A Large Set of Audio Features for Sound Description (Similarity and Classification) in the CUIDADO Project.» Technical Report; IRCAM: Paris, France, 2004.