Ling 313 - Digital Signal Processing

Analog signals are

continuous

for analog signals a challenge is that a value is

possible for every possible time point

analog signals can offer values

precise to infinite decimal points

this makes it difficult to

store access and analyze the data

analyzing analog data can be slow so to take advantage of modern computer systems you must

digitize them

the process of transforming analog data into the

digital format is called
analog-to-digital conversion

the process of analog-to-digital conversion involves

sampling
- keeps some values and dumps the rest

when sampling we decide which

values are kept and which are dumped

sampling rate set this rule as it

determines how many values (samples) are kept per second interval

if we pick 100 samples from a one-second long interval our sampling rate is

100 Hz

"The Nyquist theorem specifies that a sinuisoidal function in time or distance can be regenerated with

no loss of information as long as it is sampled at a frequency greater than or equal to twice per cycle."1

thus, the sampling rate must be the double than the

e frequency we want to capture
▶ i.e., two samples within one "period" of the wave

if we want to record up to 4000 Hz waves, we must take

8000 or more samples per second

here, the highest frequency being recorded is called the

Nyquist Frequency or Nyquist limit

When you record, you need to run an

anti-aliasing filter ▶ In modern days, this is not a thing to worry b/c most digital recorders does this automatically for us

another issue of digitization is

Quantization

Quantization

the concept that energy can occur only in discrete units called quanta

To sample this wave, what's the minimum number of samples would you take?

B.10
Because you need to take minimum two samples per cycle
so ex there was 5 cycles x2 = 10 for minimum

Human speech are mostly distributed in frequencies under 10kHz. What sampling rate would you pick to capture frequencies up to this frequency?

D. 20,000 Hz

How accurate should our Y-axis be?

▶ remember that analog signals have infinite values? ▶ again, we cannot allow infinite numbers

the higher the sample size, the more faithful the

e signal is to the analog signal

but, with higher accuracy demands

more processing power

16-bit sample size is typically enough for

acoustic analyses

Fourier Transform

It is a mathematical analysis of a complex wave into its component frequencies (proposed around 1822).

Fast Fourier Transform (FFT)

Digital technique used to process both pulsed and continuous wave Doppler signals

As the angle changes, the ratio (the sine value) also

changes

Notice that the output of the sine function is always between −1 and +1. ▶ this would mean that our a

amplitude is always 1

▶ In fact, different amplitude result from the size of the

radius of the circle (hypotenuse of the triangle) ▶ the actual amplitude is the product of the sine value and the length of the radius