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Fourier series coefficients

version 1.1 (5.35 KB) by

Calculate the Fourier series coefficients and amplitude and phase spectra.

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Calculate the Fourier coefficients of the series expansion of a function, and the amplitude and phase spectra. The script contains some theory and 3 different methods to calculate the coefficients.

USAGE
fourier_coeff(fun,t0,T)
fourier_coeff(fun,t0,T,M)
fourier_coeff(fun,t0,T,M,N)
fourier_coeff(fun,t0,T,M,N,method)
fourier_coeff(fun,t0,T,M,N,method,res)
fourier_coeff(fun,t0,T,M,N,method,res,num_P)

INPUT
- FUN: character string representing the function with "t" as the independent variable (e.g. '10*cos(2*pi*3*t-pi/4)'). Dot-arithmetic operators must be used (.* ./ .\ .^). FUN must be defined for [T0,T0+T]
- T0: initial "t" for the definition of FUN
- T: period of the function
- M: number of frequencies (default: 5)
- N: number of data points per period (default: 100)
- METHOD: 1 (least-squares), 2 (integrals [default]) or 3 (FFT)
- RES: 1 (plot results) or 0 (do not plot [default])
- NUM_P: number of periods the function will be sampled at (default: 1)

OUTPUT
- FREQ: frequencies
- COEFF: Fourier series coefficients in the form in the form [a0 a1 ... aM b1 ... bM], where f(t) = a0 + \sum_{m=1}^M { a_m cos(2pi m t/T) + b_m sin(2pi m t/T) }
So the corresponding frequencies are: 0, 1/T, 2/T, ..., M/T
- APSPEC: the first column contains the amplitude spectrum, and the second column the phase spectrum
- If RES=1:
Figure the original function and the Fourier series expansion, and another with the amplitude and phase spectra

Comments and Ratings (3)

karlosgk

karlosgk (view profile)

Very nice, thanks a lot. Do you know a way to do all this if the function is raw data?

karlosgk

karlosgk (view profile)

Fan D.Chen

Fourier series coefficients

Updates

1.1

Changed input and added screensht

MATLAB Release
MATLAB 7.10 (R2010a)

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