% m53_series.m - Explore Fourier and Chebyshev series with Chebfun


% FOURIER

F = chebfun('cos(exp(sin(t)))', [-pi,pi], 'trig')
subplot(1,2,1), plot(F,'.-')
subplot(1,2,2), plotcoeffs(F,'.-')
sum(F)
roots(F)

help cheb.gallerytrig

F = cheb.gallerytrig('FMsignal')
subplot(2,2,1), plot(F), ylim([-2 2])
subplot(2,2,3), plotcoeffs(F)

F = cheb.gallerytrig('AMsignal')
subplot(2,2,2), plot(F), ylim([-2 2])
subplot(2,2,4), plotcoeffs(F)


% CHEBYSHEV

f = chebfun('cos(exp(sin(x)))', [-pi,pi])
subplot(1,2,1), plot(f,'.-')
subplot(1,2,2), plotcoeffs(f,'.-')
sum(f)
roots(f)

help cheb.gallery

f = cheb.gallery('zigzag')
subplot(2,1,1), plot(f)
subplot(2,1,2), plotcoeffs(f)