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Fourier series coefficients

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Fourier series coefficients

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28 May 2013 (Updated )

Calculate the Fourier series coefficients and amplitude and phase spectra.

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File Information
Description

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

Required Products MATLAB
MATLAB release MATLAB 7.10 (R2010a)
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Comments and Ratings (3)
11 Jan 2014 karlosgk

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

11 Jan 2014 karlosgk  
08 Dec 2013 Fan D.Chen

Fourier series coefficients

Updates
03 Jun 2013

Changed input and added screensht

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