def IDFT(X):
"""
Input:
X (numpy array) = frequency spectrum (length N)
Output:
The function should return a numpy array of length N
x (numpy array) = The N point IDFT of the frequency spectrum X
"""
x = np.array([])
N = len(X)
for i in range(N):
idx = np.arange(0,N)
# s = 1.0*np.exp(1j*(2.0*math.pi*i*idx/N))
s = A2Part2.genComplexSine(-i, N)
x = np.append(x,np.sum(X*s))
return x/N
# X = np.array([1 ,1 ,1 ,1])
#
# print 'IDFT of X: '
# print IDFT(X)
def DFT(x):
"""
Input:
x (numpy array) = input sequence of length N
Output:
The function should return a numpy array of length N
X (numpy array) = The N point DFT of the input sequence x
"""
## Your code here
X=np.array([])
N=np.size(x)
for k in np.arange(N):
X=np.append(X, sum(x * a22.genComplexSine(k, N)))
return (X)
def DFT(x):
"""
Input:
x (numpy array) = input sequence of length N
Output:
The function should return a numpy array of length N
X (numpy array) = The N point DFT of the input sequence x
"""
## Your code here
X = np.array([])
N = np.size(x)
for k in np.arange(N):
X = np.append(X, sum(x * a22.genComplexSine(k, N)))
return (X)
def genMagSpec(x):
"""
Input:
x (numpy array) = input sequence of length N
Output:
The function should return a numpy array
magX (numpy array) = The magnitude spectrum of the input sequence x
(length N)
"""
## Your code here
X=np.array([])
N=np.size(x)
for k in np.arange(N):
X=np.append(X, abs(sum(x * a22.genComplexSine(k, N))))
return (X)
def DFT(x):
"""
Input:
x (numpy array) = input sequence of length N
Output:
The function should return a numpy array of length N
X (numpy array) = The N point DFT of the input sequence x
"""
## Your code here
N = x.size
X = np.array([])
for k in range(N):
s = A2Part2.genComplexSine(k, N)
X = np.append(X, sum(x*s))
return X
def DFT(x):
"""
Input:
x (numpy array) = input sequence of length N
Output:
The function should return a numpy array of length N
X (numpy array) = The N point DFT of the input sequence x
"""
X = np.array([])
N = len(x)
for k in range(N):
s = A2Part2.genComplexSine(k, N)
X = np.append(X, np.sum(x * s))
# bOutput = True
# validationOutput(bOutput, X)
return X
def IDFT(X):
"""
Input:
X (numpy array) = frequency spectrum (length N)
Output:
The function should return a numpy array of length N
x (numpy array) = The N point IDFT of the frequency spectrum X
"""
## Your code here
N = X.size
x = np.array([])
k = np.arange(N)
print k
for n in range(N):
s = np.conjugate(A2Part2.genComplexSine(n, N))
#s = np.exp(1j * 2 * np.pi * k * n / N)
x = np.append(x, 1.0 / N * sum(X * s))
return x
def IDFT(X):
"""
Input:
X (numpy array) = frequency spectrum (length N)
Output:
The function should return a numpy array of length N
x (numpy array) = The N point IDFT of the frequency spectrum X
"""
## Your code here
# DFT = X[k] = 1/N * SUM (x[n] * e ^ 2pi*k*n/N) k = 0 .. N-1
N = len(X)
x = np.zeros(N, complex)
for k in range(0,N):
# Find cross-correlation between the signal and a set of N complex sinusoids
# Multiply each point in the signal with a complex sinusoid. Since sinusoids are orthogonal,
# the result of the multiplication will be non-zero only if the sinusoid is present in the signal
#x[k] = sum(X * genComplexISine(k,N)) / N
x[k] = sum(X * A2Part2.genComplexSine(-k,N)) / N #IDFT is same as DFT but with -ve frequencies and a factor of 1/N
return x
def IDFT(X):
"""
Input:
X (numpy array) = frequency spectrum (length N)
Output:
The function should return a numpy array of length N
x (numpy array) = The N point IDFT of the frequency spectrum X
"""
## Your code here
N = len(X)
x = np.empty(0, dtype=complex)
for n in xrange(N):
complexSine = np.conjugate(A2.genComplexSine(n, N))
x = np.append(x, [X[0]])
for k in xrange(1, N):
x[n] = x[n] + X[k] * complexSine[k]
return (x / N)
def DFT(x):
"""
Input:
x (numpy array) = input sequence of length N
Output:
The function should return a numpy array of length N
X (numpy array) = The N point DFT of the input sequence x
"""
## Your code here
N = len(x)
X = np.empty(0,dtype = complex)
for k in xrange(N):
complexSine = A2.genComplexSine(k,N)
X = np.append( X , [x[0] + 0 * 1j])
for n in xrange(1,N):
X[k] = X[k] + x[n] * complexSine[n]
return X
import A2Part1
import A2Part2
import A2Part3
import A2Part4
import A2Part5
import numpy
print ("Number 1: ", A2Part1.genSine(1.0, 10.0, 1.0, 50.0, 0.1))
print ("Number 2: ", A2Part2.genComplexSine(1,5))
print ("Number 3: ", A2Part3.DFT(numpy.array([1,2,3,4])))
print ("Number 4: ", A2Part4.IDFT(numpy.array([1,1,1,1])))
print ("Number 4a: ", A2Part4.IDFT(A2Part3.DFT(numpy.array([1,2,3,4]))))
print ("Number 4b: ", A2Part4.IDFT(A2Part3.DFT(A2Part4.IDFT(A2Part3.DFT(numpy.array([1,2,3,4]))))))
print ("Number 5: ", A2Part5.genMagSpec(numpy.array([1,2,3,4])))
