This is a Discrete Fourier Transformation calculation using matrix mutiplication

dft.py

def omega(N,k,n):
	return np.exp(-2*np.pi/N*k*n*1j)

def hanWindow(N):
	diag=np.array([np.sin(np.pi*i/(N-1))**2 for i in range(N)])
	H=np.diag(diag)
	return H

def createF(N):
	F=np.zeros((N,N),dtype=complex)
	for i in range(N):
		for j in range(N):
			F[i,j]=omega(N,j,i)
	return F

def createA(N,input_length,hop):
	FH=np.dot(createF(N),hanWindow(N))
	A=np.zeros(((2*input_length-1)*N,input_length*N),dtype=complex)

	for i in range(2*input_length-1):
		A[i*N:(i+1)*N,i*hop:i*hop+N]=FH
	return A

def DFT(N,hop,input_data):
	'''
	N: DFT window
	hop: hop size
	input_data: signal
	'''
	input_length=int(len(input_data)/N)
	print "Using BIG matrix to do spectrogram analysis"
	print "The size of input data is:",input_length*N
	A=createA(N,input_length,hop)
	plot_matrix(A)

	DFT_coeff=np.dot(A,input_data[:input_length*N])
	
	spectrogram=[]
	for i in range(2*input_length-1):
		spectrogram.append(np.abs(DFT_coeff[i*N:i*N+N/2]))
	
	spectrogram=np.array(spectrogram)
	return spectrogram