zeroPadPhaseDFT.py

import numpy as np
import math
from scipy.signal import get_window


def DFT(x, fs, a_time):
	"""
	Input:
	x (numpy array) = input sequence of length N
	fs (int) = sampling frequency in Hz
	a_time (float) = time index in seconds
	Output:
	The function should return a numpy array of length N
	X (numpy array) = The N point DFT of the input sequence x
	mX (numpy array) = magnitude spectrum
	pX (numpy array) = phase spectrum
	"""
	dftbuffer = zeroPadZeroPhase(x, fs, a_time)
	N = len(dftbuffer)
	X = np.array([(np.sum(dftbuffer*genComplexSine(k, N))) for k in range(N)])
	mX = 20 * np.log10(abs(X))
	pX = np.angle(X)
	return X, mX, pX


def genComplexSine(k, N):
	"""
	Inputs:
	k (integer) = frequency index of the complex sinusoid of the DFT
	N (integer) = length of complex sinusoid in samples
	Output:
	The function should return a numpy array
	cSine (numpy array) = The generated complex sinusoid (length N)
	"""
	n = np.arange(N)
	cSine = np.exp(-1j * 2 * np.pi * k * n / N)
	return cSine


def zeroPadZeroPhase(x, fs, a_time):
	"""
	Inputs:
	x (numpy array) = input signal of length M
	fs (float) = sampling frequency in Hz
	a_time (float) = time index in seconds
	Output:
	The function should return
	dftbuffer (numpy array) = windowed signal of N size
	"""
	O = 511
	w = get_window("blackman", O)

	# Allocate and populate buffer
	M = len(x)
	N = 8 * O
	sample = int(a_time*fs) # get sample
	x1 = x[sample:sample+O] 
	dft_size = 1024
	hM1 = (w.size+1)//2
	hM2 = int(math.floor(w.size/2))
	dftbuffer = np.zeros(N)
	xw = x1*w 
	dftbuffer[:hM1] = xw[hM2:]
	dftbuffer[-hM2:] = xw[:hM2] 
	return dftbuffer