Engee documentation

powerbw

Power bandwidth.

Library

EngeeDSP

Syntax

Function call

  • bw = powerbw(x) — returns the bandwidth (at half power level) bw at the level of 3 dB of input signal x. The function calculates the bandwidth at the level of 3 dB from the periodogram of the signal x.

  • bw = powerbw(x,Fs) — returns the bandwidth at the level of 3 dB, expressed in terms of the sampling rate Fs.

  • bw = powerbw(pxx,f) — returns the bandwidth at the level of 3 dB for Power spectral density (SPM) estimation pxx. Frequencies f correspond to the estimates in pxx.

  • bw = powerbw(sxx,f,rbw) — calculates the bandwidth at the level of 3 dB power spectrum estimates sxx at the level of 3 dB. Frequencies f correspond to the estimates in sxx. The function uses the bandwidth of the resolution rbw to integrate each power estimate.

  • bw = powerbw(___,freqlims,r) — defines the frequency range in which the reference level is calculated. This syntax can include any combination of input arguments from the previous options, provided that the second input argument is either Fs, or f. If the second input argument is passed as empty, powerbw assumes a normalized frequency. The function calculates the frequency difference between the points where the spectrum falls below the reference level by r dB or reaches the end point.

  • bw,flo,fhi,power = powerbw(___) — also returns the lower and upper limits of the power bandwidth and the power within these limits.

  • powerbw(___) — without output arguments, plots the SPM or power spectrum in the current graph window and annotates the bandwidth.

Arguments

Input arguments

# x — input signal

+ vector | the matrix

Details

An input signal specified as a vector or matrix. If x — vector, it is considered as a single channel. If x — the matrix, then the function powerbw calculates the power bandwidth independently for each column. x it must be finite-valued.

Типы данных

Float32, Float64

# Fs — sampling rate
positive real scalar

Details

The sampling frequency, set as a positive real scalar. The sampling rate is the number of samples per unit of time. If time is measured in seconds, then the sampling frequency is indicated in hertz.

Типы данных

Float32, Float64

# pxx — spectral power density

+ vector | the matrix

Details

An estimate of the spectral power density (SPM), defined as a vector or matrix. If pxx — one-sided evaluation, then it must correspond to the actual signal. If pxx — the matrix, then powerbw calculates the bandwidth of each column pxx regardless.

The power spectral density should be expressed in linear units, not in decibels. Use the function db2pow to convert decibel values to power values.

Типы данных

Float32, Float64

# f — frequencies

+ vector

Details

Frequencies specified as a vector. If the first element is f equal to 0 Then powerbw assumes that the spectrum is a one-way spectrum of a real signal. In other words, the function doubles the power value in the zero frequency bin, aiming for the point 3 dB.

Типы данных

Float32, Float64

# sxx — power spectrum estimation

+ vector | the matrix

Details

An estimate of the power spectrum, specified as a vector or matrix. If sxx — the matrix, then powerbw calculates the bandwidth of each column sxx regardless.

The power spectrum should be expressed in linear units, not in decibels. Use the function db2pow to convert decibel values to power values.

Типы данных

Float32, Float64

# rbw — resolution band

+ positive scalar

Details

The resolution band is set as a positive scalar. The resolution band is the product of two quantities: the frequency resolution of the discrete Fourier transform and the equivalent noise band of the window used to calculate the SPM.

Типы данных

Float32, Float64

# freqlims — frequency limits

+ two-element vector

Details

Frequency limits set as a two-element vector of real values. If the argument is freqlims If set, the reference level will be the average power level in the reference band. If the argument is freqlims If not specified, the reference level will be the maximum power level in the spectrum. Meaning freqlims must be within the target band.

Типы данных

Float32, Float64

# r — power level drop

+ 10*log10(2) (by default) | positive real scalar

Details

The power level drop, given as a positive real scalar, expressed in dB.

Типы данных

Float32, Float64

Name-value input arguments

# 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

# bw — power bandwidth

+ scalar | vector

Details

The power bandwidth returned as a scalar or vector.

  • If the sampling rate is specified, then bw it has the same units of measurement as Fs.

  • If the sampling frequency is not specified, then bw it has units of measurement of rad/count.

# flo,fhi — frequency bandwidth limits

+ scalars | vectors

Details

The frequency bandwidth boundaries returned as scalars or vectors.

# power — power stored in the bandwidth

+ scalar | vector

Details

The power stored in the bandwidth returned as a scalar or vector.

Examples

Bandwidth-limited signals

Details

We will generate a signal whose SPM resembles the frequency response of a bandpass FIR filter. 88-th order with normalized cutoff frequencies rad/countdown and rad/countdown.

import EngeeDSP.Functions: fir1

d = fir1(88, [0.25 0.45])

Calculate the occupied signal band at the level of 3 dB. We will specify as a reference level the average power in the range from rad/countdown to rad/countdown. Let’s build a schedule for the SPM.

import EngeeDSP.Functions: powerbw

powerbw(d, [], [0.2 0.6]*pi, 3, out=:plot)

powerbw 1

We will output the bandwidth, its lower and upper limits, as well as the bandwidth power. Specifying the sampling rate it is equivalent to leaving it unidentified.

bw, flo, fhi, power = powerbw(d, 2π, [0.2, 0.6] * π)
println([" bw"; "flo"; "fhi"] .* " = " .* string.([bw; flo; fhi] / π) .* "π")
[" bw = 0.20047359178514887π", "flo = 0.24995529776303813π", "fhi = 0.450428889548187π"]
import EngeeDSP.Functions: bandpower

println("power = ", round((power/bandpower(d)*100)[1], digits=1), "% of total")
power = 96.9% of total

Add a second channel with normalized cutoff frequencies rad/countdown and rad/count and an amplitude of one tenth of the amplitude of the first channel.

d = [d fir1(88, [0.5 0.8])/10]

Let’s calculate the bandwidth of a two-channel signal at the level of 6 dB. We will specify the maximum power level of the spectrum as a reference level.

powerbw(d, [], [], 6, out=:plot)

powerbw 2

Let’s output the bandwidth of each channel at the level of 6 dB, as well as the lower and upper limits.

bw, flo, fhi = powerbw(d, [], [], 6)
bds = [bw[1] bw[2]; flo[1] flo[2]; fhi[1] fhi[2]]
labels = [" bw", "flo", "fhi"]

for channel in 1:2
    for i in 1:3
        println(labels[i] * " (ch_$channel) = $(round(bds[i, channel] / π, digits=5))π")
    end
end
 bw (ch_1) = 0.19794π
flo (ch_1) = 0.25176π
fhi (ch_1) = 0.44971π
 bw (ch_2) = 0.29418π
flo (ch_2) = 0.50271π
fhi (ch_2) = 0.79689π

Algorithms

To determine the bandwidth at the level of 3 dB function powerbw Calculates an estimate of the periodogram’s power spectrum using a rectangular window and uses the highest estimate as a reference level. Bandwidth is the frequency difference between points where the spectrum drops by at least 3 dB relative to the reference level. If the signal reaches one of its endpoints before descending to 3 dB, function powerbw uses this endpoint to calculate the difference.

The same bandwidth value per level 3 dB, bw, can be obtained from the signal x with sampling rate Fs in three ways.

Straight from the signal

bw = powerbw(x,Fs)

From the periodogram of the signal

P,F = periodogram(x,[],length(x),Fs);

bw = powerbw(P,F)

From the estimation of the spectral power (SPM Welch) of the signal

P,F = pwelch(x,rectwin(length(x)),[],length(x),Fs);

bw = powerbw(P,F)
Because powerbw It uses an intermediate representation to convert the input signal from the time domain to the frequency domain. The bandwidth of the returned power may vary depending on the signal conversion method, the number of DFT points, and the window size.