From 06b7d461e4cba19b4116ea9cedc26a461748d885 Mon Sep 17 00:00:00 2001
From: Erik Strand <erik.strand@cba.mit.edu>
Date: Wed, 8 May 2019 17:44:46 -0400
Subject: [PATCH] Plot DCT
---
compressed_sensing.py | 26 ++++++++++++++++++++------
1 file changed, 20 insertions(+), 6 deletions(-)
diff --git a/compressed_sensing.py b/compressed_sensing.py
index 360d74a..b962029 100644
--- a/compressed_sensing.py
+++ b/compressed_sensing.py
@@ -1,4 +1,5 @@
import numpy as np
+import scipy
import matplotlib.pyplot as plt
@@ -6,22 +7,35 @@ def sample_two_sins(f1, f2, sample_times):
sample_rads = 2 * np.pi * sample_times
return np.sin(f1 * sample_rads) + np.sin(f2 * sample_rads)
+
+def compute_dct_matrix(n_samples):
+ dct_matrix = np.zeros((n_samples, n_samples))
+ root_one_over_n = np.sqrt(1.0 / n_samples)
+ root_two_over_n = np.sqrt(2.0 / n_samples)
+ for j in range(0, n_samples):
+ dct_matrix[0, j] = root_one_over_n
+ for i in range(1, n_samples):
+ for j in range(0, n_samples):
+ dct_matrix[i, j] = root_two_over_n * np.cos(np.pi * (2 * j + 1) * i / (2 * n_samples))
+ return dct_matrix
+
+
if __name__ == "__main__":
f1 = 697 # Hz
f2 = 1209 # Hz
+ # Part (a)
sample_period = 0.01
- n_samples = 1000
+ n_samples = 250
sample_times = (sample_period / n_samples) * np.arange(n_samples)
sample_values = sample_two_sins(f1, f2, sample_times)
plt.plot(sample_times, sample_values)
plt.savefig("fig_a.png")
plt.close()
- sample_period = 0.02
- n_samples = 1000
- sample_times = (sample_period / n_samples) * np.arange(n_samples)
- sample_values = sample_two_sins(f1, f2, sample_times)
- plt.plot(sample_times, sample_values)
+ # Part (b)
+ dct_matrix = compute_dct_matrix(n_samples)
+ dct = np.matmul(dct_matrix, sample_values)
+ plt.plot(np.arange(n_samples), dct)
plt.savefig("fig_b.png")
plt.close()
--
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