lab #8 follow-up: sounds and signals* * figures from kaplan, d. (2003) introduction to scientific...
TRANSCRIPT
Lab #8 Follow-Up:
Sounds and Signals*
* Figures from Kaplan, D. (2003) Introduction to Scientific Computation and Programming CLI Engineering.
• Recall transducer concept convert input signal
into numbers.
• Signal: a quantity that changes over time– Body temperature– Air pressure (sound)– Electrical potential on skin (electrocardiogram)– Seismological disturbances– Stock prices
Intro to Sounds & Signals
• We will study audio signals (sounds), but the same issues apply across a broad range of signal types.
• Two different approaches to doing the same thing:
– Commercial GUI program (Audacity, Pro Tools)– Programmatic (Python)
Intro to Sounds & Signals
13.1 Basics of Computer Sound>>> x, fs, bits = wavread("fh.wav")>>> len(x)41777 >>> min(x), max(x)('\x00', '\xff')>>> fs11025>>> bits8
Basics of Computer Sound
Basics of Computer Sound
Basics of Computer Sound
• x contains the sound waveform (signal) – essentially, voltage levels representing transduced air pressure on microphone.
• fs is the sampling frequency (rate) – how many time per second (Hertz, Hz), did we measure the voltage?
• bits is the number of bits used to represent each sample.
Questions
• Why does the sound waveform range from hexadecimal 00 to FF, whereas we plot it as -1 to +1?
– These values are essentially arbitrary. One nice feature of a ±x representation is that zero means silence. But the audio player likes values between 0 and 255.
• What role does the sampling frequency play in the quality of the sound?– The more samples per second, the closer the
sound is to a “perfect” recording.
Questions
• What happens if we double (or halve) the sampling frequency at playback, and why?
• What is it about the waveform that determines the sound we're hearing (which vowel), and the speaker's voice?
Questions
• What is it about the waveform that determines the sound we're hearing (which vowel), and the speaker's voice?–Most of this information is encoded in the
frequencies that make up the waveform – roughly, the differences between locations of successive peaks – and not in the actual waveform values themselves.
–We can do some useful processing on the “raw” waveform, however – e.g., count syllables:
Syllable Counting by Smoothing and Peak-Picking
Perception and Generation of Sound
• Sound is the perception of small, rapid vibrations in air pressure on the ear.
• Simplest model of sound is a function P(t) expressing pressure P at time t:
P(t) = A sin(2πft + φ)
where A = amplitude (roughly, loudness)
f = frequency (cycles per second)φ = phase (roughly, starting point)
• This is the equation for a pure musical tone (just one pitch)
Perception and Generation of Sound
– Inverse of frequency is period (distance between peaks):
Perception and Generation of Sound
–E.g., whistling a musical scale:
Transducing and Recording Sound
• Convert sound pressure to voltage, then digitize voltage into N discrete values in interval [x
min, x
max], by sampling at frequency F
s.
• This is done by a analog /digital converter.• Another device must pre-amplify sound to match
input expectations of a/d converter.• N is typically a power of 2, so we can use bits to
express sampling precision (minimum 8 for decent quality). This is called quantization.
• Various things can go wrong if we don't choose these values wisely....
A segment of the sound “OH” transduced to voltage.
Top: The preamplifier has been set appropriately so that the analog voltage signal takes up a large fraction of the A/D voltage range. The digitized signal closely resembles the analog signal even though the A/D conversion is set to 8 bits.
Bottom: The preamplifier has been set too low. Consequently, there is effectively only about 3 bits of resolution in the digitized signal; most of the range is unused.
Transducing and Recording Sound
0 2 4 6 8 10 12 14-4
-2
0
2
4
Vol
tage
Appropriate preamplification
0 2 4 6 8 10 12 14-96
-64
-32
0
32
64
96
A/D
uni
ts
AnalogDigital
0 2 4 6 8 10 12 14
-0.1
0
0.1
Vol
tage
Time (ms)
Preamplification too low
0 2 4 6 8 10 12 14
-4
-2
0
2
4
A/D
uni
ts
Figure 13.6.
Clipping of a signal (right) when the preamplifier has been set too high, so that the signal is outside of the −5 to 5 V range of the A/D converter.
Transducing and Recording Sound
Aliasing and the Sampling Frequency• Someone has an alias when they use more than
one name (representation)• In the world of signals, this means having more
than one representation of an analog signal, because of inadequate sampling frequency
• Familiar visual aliasing from the movies (when 32 frames per second is too slow)• Wagon wheel / propeller going backwards• Scan lines appearing on computer screen
• Inadequate Fs can result in aliasing for sounds
too....
Aliasing and the Sampling Frequency
Aliasing and the Sampling Frequency
Aliasing. A set of samples marked as circles. The three sine waves plotted are of different frequencies, but all pass through the same samples. The aliased frequencies are F +m/∆T, where m is any integer and ∆T is the sampling interval. The sine waves shown are m = 0, m = 1, and m = 2. 0 1 2 3
-1
0
1
Time (T)
Am
plitu
de
m = 0m = 1m = 2samples
Aliasing and the Sampling Frequency
• Nyquist's Theorem tells us that Fs should be at
least twice the maximum frequency Fmax
we wish to reproduce.
• Intuitively, we need two values to represent a single cycle: one for peak, one for valley:
