Week 2 - Digital signal processing

Digital Signal Processors (DSPs) take real-world signals like voice, audio, video, temperature, pressure, or position that have been digitized and then mathematically manipulate them.

• Converters such as an analogue-to-digital converter then take the real-world signal and encodes it in binary (1's and 0's).
• DSP takes over here and captures the digitized information and processing it. It then feeds the digitized information back for use in the real world.
• It does this in one of two ways, either digitally or in an analogue format by going through a Digital-to-analogue converter.

• A low-pass filter is an electronic filter that passes low-frequency signals but attenuates (reduces the amplitude of) signals with frequencies higher than the cutoff frequency. 
• In smoothing, the data points of a signal are modified so that individual points that are higher than the immediately adjacent points (presumably because of noise) are reduced, and points that are lower than the adjacent points are increased. This naturally leads to a smoother signal. As long as the true underlying signal is actually smooth, then the true signal will not be much distorted by smoothing, but the noise will be reduced.

Pitch

The sensation of a frequency is commonly referred to as the pitch of a sound. 

A high pitch sound corresponds to a high frequency sound wave and a low pitch sound corresponds to a low frequency sound wave. 

DSP 1. Precision

In theory the precision of Digital Signal Processing systems is limited only be the conversion process at input and output (analogue to Digital and Digital to analogue).

In practice, sampling rate (sampling frequency) and word length restrictions (number of bits) modify this. 

DSP 2. Robustness

Due to logic level noise margins, digital systems are inherently less susceptible to:

1. Electrical noise (pick-up)
2. Components tolerance variations

DSP 3. Flexibility

Programmability allows upgrading and expansion of the processing operations, without necessarily incurring large scale hardware changes.

Practical systems with desired Time Varying and / or Adaptive characteristics can be constructed.

How a Sound card works

• Sounds and computer data are fundamentally different. 
• Sounds are analogue - they are made of waves that travel through matter. 
• People hear sounds when these waves physically vibrate their eardrums. 
• Computers, however, communicate digitally, using electrical impulses that represent 0s and 1s. 
• A sound card translates between a computer's digital information and the outside world's analogue

Sampling rate

Sample rate indicates the number of digital samples taken of an audio signal each second. 

This rate determines the frequency range of an audio file. 

The higher the sample rate, the closer the shape of the digital waveform is to that of the original analog waveform.

To reproduce a given frequency, the sample rate must be at least twice that frequency.

CDs have a sampling rate of 44.1KHz so they can reproduce frequencies up to 22.05KHz, which is just beyond the limit of human hearing, 20KHz.

Bit depth

When a waveform is sampled each sample is assigned the amplitude value closest to the original analogue wave

CD quality sound is 16bit which means that each sample has 65,536 possible amplitude values.

DVD quality sound is 24bit which means that each sample has 16,777,216 possible values.

Dynamic range

The ratio of the Largest Signal Amplitude to the Smallest, is known as the Dynamic Range.

Since a 16 bit Word length allows 216 (i.e. 65536) different signal levels the dynamic range (DR) is calculated as

DR = 20log([ Voltage Range] / [ quantisation Step Size]) dB

=20log(216) dB

= 96 dB