Fix

code/thinkdsp.py

@@ -59,7 +59,7 @@ def __init__(self, filename='sound.wav', framerate=11025):
         self.fp.setnchannels(self.nchannels)
         self.fp.setsampwidth(self.sampwidth)
         self.fp.setframerate(self.framerate)
-    
+
     def write(self, wave):
         """Writes a wave.
 
@@ -92,14 +92,14 @@ def read_wave(filename='sound.wav'):
     nframes = fp.getnframes()
     sampwidth = fp.getsampwidth()
     framerate = fp.getframerate()
-    
+
     z_str = fp.readframes(nframes)
-    
+
     fp.close()
 
     dtype_map = {1:numpy.int8, 2:numpy.int16}
     assert sampwidth in dtype_map
-    
+
     ys = numpy.fromstring(z_str, dtype=dtype_map[sampwidth])
     wave = Wave(ys, framerate)
     return wave
@@ -123,23 +123,23 @@ class _SpectrumParent(object):
     @property
     def max_freq(self):
         return self.framerate / 2.0
-        
+
     @property
     def freq_res(self):
         return self.max_freq / (len(self.fs) - 1)
 
     def plot(self, low=0, high=None, **options):
         """Plots amplitude vs frequency.
 
-        low: int index to start at 
+        low: int index to start at
         high: int index to end at
         """
         thinkplot.plot(self.fs[low:high], self.amps[low:high], **options)
 
     def plot_power(self, low=0, high=None, **options):
         """Plots power vs frequency.
 
-        low: int index to start at 
+        low: int index to start at
         high: int index to end at
         """
         thinkplot.plot(self.fs[low:high], self.power[low:high], **options)
@@ -183,7 +183,7 @@ def __add__(self, other):
         return Spectrum(hs, self.framerate)
 
     __radd__ = __add__
-        
+
 
     @property
     def real(self):
@@ -271,7 +271,7 @@ def make_wave(self):
 
 class IntegratedSpectrum(object):
     """Represents the integral of a spectrum."""
-    
+
     def __init__(self, cs, fs):
         """Initializes an integrated spectrum:
 
@@ -284,7 +284,7 @@ def __init__(self, cs, fs):
     def plot_power(self, low=0, high=None, expo=False, **options):
         """Plots the integrated spectrum.
 
-        low: int index to start at 
+        low: int index to start at
         high: int index to end at
         """
         cs = self.cs[low:high]
@@ -400,7 +400,7 @@ def make_wave(self):
         for t, spectrum in sorted(self.spec_map.iteritems()):
             wave = spectrum.make_wave()
             n = len(wave)
-            
+
             if self.window_func:
                 window = 1 / self.window_func(n)
                 wave.window(window)
@@ -453,7 +453,7 @@ def __or__(self, other):
         """Concatenates two waves.
 
         other: Wave
-        
+
         returns: Wave
         """
         if self.framerate != other.framerate:
@@ -567,8 +567,12 @@ def plot(self, **options):
         """Plots the wave.
 
         """
-        n = len(self.ys)
-        ts = numpy.linspace(0, self.duration, n)
+        dt = 1.0 / self.framerate
+        ts = numpy.arange(self.start, self.start + self.duration, dt)
+        # Due to erroneous division, the ts calculated above and below
+        # have slightly different elements
+        #n = len(self.ys)
+        #ts = numpy.linspace(self.start, self.start + self.duration, n)
         thinkplot.plot(ts, self.ys, **options)
 
     def corr(self, other):
@@ -581,7 +585,7 @@ def corr(self, other):
         mat = self.cov_mat(other)
         corr = mat[0][1] / math.sqrt(mat[0][0] * mat[1][1])
         return corr
-        
+
     def cov_mat(self, other):
         """Covariance matrix of two waves.
 
@@ -680,7 +684,7 @@ def quantize(ys, bound, dtype):
     if max(ys) > 1 or min(ys) < -1:
         print 'Warning: normalizing before quantizing.'
         ys = normalize(ys)
-        
+
     zs = (ys * bound).astype(dtype)
     return zs
 
@@ -749,7 +753,7 @@ def plot(self, framerate=11025):
         duration = self.period * 3
         wave = self.make_wave(duration, start=0, framerate=framerate)
         wave.plot()
-    
+
     def make_wave(self, duration=1, start=0, framerate=11025):
         """Makes a Wave object.
 
@@ -760,7 +764,7 @@ def make_wave(self, duration=1, start=0, framerate=11025):
         returns: Wave
         """
         dt = 1.0 / framerate
-        ts = numpy.arange(start, duration, dt)
+        ts = numpy.arange(start, start + duration, dt)
         ys = self.evaluate(ts)
         return Wave(ys, framerate=framerate, start=start)
 
@@ -781,7 +785,7 @@ def infer_framerate(ts):
 
 class SumSignal(Signal):
     """Represents the sum of signals."""
-    
+
     def __init__(self, *args):
         """Initializes the sum.
 
@@ -806,15 +810,15 @@ def evaluate(self, ts):
         """Evaluates the signal at the given times.
 
         ts: float array of times
-        
+
         returns: float wave array
         """
         return sum(sig.evaluate(ts) for sig in self.signals)
 
 
 class Sinusoid(Signal):
     """Represents a sinusoidal signal."""
-    
+
     def __init__(self, freq=440, amp=1.0, offset=0, func=numpy.sin):
         """Initializes a sinusoidal signal.
 
@@ -840,7 +844,7 @@ def evaluate(self, ts):
         """Evaluates the signal at the given times.
 
         ts: float array of times
-        
+
         returns: float wave array
         """
         phases = PI2 * self.freq * ts + self.offset
@@ -854,7 +858,7 @@ def CosSignal(freq=440, amp=1.0, offset=0):
     freq: float frequency in Hz
     amp: float amplitude, 1.0 is nominal max
     offset: float phase offset in radians
-    
+
     returns: Sinusoid object
     """
     return Sinusoid(freq, amp, offset, func=numpy.cos)
@@ -866,20 +870,20 @@ def SinSignal(freq=440, amp=1.0, offset=0):
     freq: float frequency in Hz
     amp: float amplitude, 1.0 is nominal max
     offset: float phase offset in radians
-    
+
     returns: Sinusoid object
     """
     return Sinusoid(freq, amp, offset, func=numpy.sin)
 
 
 class SquareSignal(Sinusoid):
     """Represents a square signal."""
-    
+
     def evaluate(self, ts):
         """Evaluates the signal at the given times.
 
         ts: float array of times
-        
+
         returns: float wave array
         """
         cycles = self.freq * ts + self.offset / PI2
@@ -890,12 +894,12 @@ def evaluate(self, ts):
 
 class SawtoothSignal(Sinusoid):
     """Represents a sawtooth signal."""
-    
+
     def evaluate(self, ts):
         """Evaluates the signal at the given times.
 
         ts: float array of times
-        
+
         returns: float wave array
         """
         cycles = self.freq * ts + self.offset / PI2
@@ -906,12 +910,12 @@ def evaluate(self, ts):
 
 class ParabolicSignal(Sinusoid):
     """Represents a parabolic signal."""
-    
+
     def evaluate(self, ts):
         """Evaluates the signal at the given times.
 
         ts: float array of times
-        
+
         returns: float wave array
         """
         cycles = self.freq * ts + self.offset / PI2
@@ -923,12 +927,12 @@ def evaluate(self, ts):
 
 class GlottalSignal(Sinusoid):
     """Represents a periodic signal that resembles a glottal signal."""
-    
+
     def evaluate(self, ts):
         """Evaluates the signal at the given times.
 
         ts: float array of times
-        
+
         returns: float wave array
         """
         cycles = self.freq * ts + self.offset / PI2
@@ -940,12 +944,12 @@ def evaluate(self, ts):
 
 class TriangleSignal(Sinusoid):
     """Represents a triangle signal."""
-    
+
     def evaluate(self, ts):
         """Evaluates the signal at the given times.
 
         ts: float array of times
-        
+
         returns: float wave array
         """
         cycles = self.freq * ts + self.offset / PI2
@@ -957,7 +961,7 @@ def evaluate(self, ts):
 
 class Chirp(Signal):
     """Represents a signal with variable frequency."""
-    
+
     def __init__(self, start=440, end=880, amp=1.0):
         """Initializes a linear chirp.
 
@@ -981,7 +985,7 @@ def evaluate(self, ts):
         """Evaluates the signal at the given times.
 
         ts: float array of times
-        
+
         returns: float wave array
         """
         freqs = numpy.linspace(self.start, self.end, len(ts)-1)
@@ -1005,12 +1009,12 @@ def _evaluate(self, ts, freqs):
 
 class ExpoChirp(Chirp):
     """Represents a signal with varying frequency."""
-    
+
     def evaluate(self, ts):
         """Evaluates the signal at the given times.
 
         ts: float array of times
-        
+
         returns: float wave array
         """
         start, end = math.log10(self.start), math.log10(self.end)
@@ -1020,20 +1024,20 @@ def evaluate(self, ts):
 
 class SilentSignal(Signal):
     """Represents silence."""
-    
+
     def evaluate(self, ts):
         """Evaluates the signal at the given times.
 
         ts: float array of times
-        
+
         returns: float wave array
         """
         return numpy.zeros(len(ts))
 
 
 class _Noise(Signal):
     """Represents a noise signal (abstract parent class)."""
-    
+
     def __init__(self, amp=1.0):
         """Initializes a white noise signal.
 
@@ -1057,7 +1061,7 @@ def evaluate(self, ts):
         """Evaluates the signal at the given times.
 
         ts: float array of times
-        
+
         returns: float wave array
         """
         ys = numpy.random.uniform(-self.amp, self.amp, len(ts))
@@ -1071,7 +1075,7 @@ def evaluate(self, ts):
         """Evaluates the signal at the given times.
 
         ts: float array of times
-        
+
         returns: float wave array
         """
         ys = numpy.random.normal(0, 1, len(ts))
@@ -1089,7 +1093,7 @@ def evaluate(self, ts):
         a uniform random series.
 
         ts: float array of times
-        
+
         returns: float wave array
         """
         #dys = numpy.random.normal(0, 1, len(ts))
@@ -1182,7 +1186,7 @@ def midi_to_freq(midi_num):
     """Converts MIDI note number to frequency.
 
     midi_num: int MIDI note number
-    
+
     returns: float frequency in Hz
     """
     x = (midi_num - 69) / 12.0
@@ -1240,7 +1244,7 @@ def main():
     return
 
     wfile = WavFileWriter()
-    for sig_cons in [SinSignal, TriangleSignal, SawtoothSignal, 
+    for sig_cons in [SinSignal, TriangleSignal, SawtoothSignal,
                      GlottalSignal, ParabolicSignal, SquareSignal]:
         print sig_cons
         sig = sig_cons(440)

trunk/book.tex

@@ -451,7 +451,7 @@ \section{Signals}
 starts at $\cos \pi/2$, which is 0.
 A sine signal with
 {\tt offset=0} also starts at 0.  In fact,
-a cosine signal with {\tt offset=pi/2} is identical to a sine
+a sine signal with {\tt offset=pi/2} is identical to a cosine
 signal with {\tt offset=0}.
 
 Signals have an \verb"__add__" method, so you can use the {\tt +}