What is the roadmap of signal manipulation and processing?
(Input)
1. Sensing Unit
(Sensor Output)
2. Filter
3. Sample and Hold
4. ADC
(Digitised Signal)
5. Processing Unit
Signals from the sensor undergo filtering followed by digitisation.
- Digitisation is performed using a series of steps including Discretisation, Sample holding and ADC
- The digitised signal is further processed to extract information.
- The final output is generally the analog form of the digitised, processed signal. Digital to Analog conversion is used to convert the digital signal back to analog signal
What is a continuous-time signals and what is it represented by?
A signal that is defined and has a value at every instant of time within a given interval, represented by x(t)
The amplitude of a continuous-time signal…
takes any value from a continuous range of real numbers
What else are continuous-time signals known as?
They are known as analog signals (their amplitude is “analogous”- proportional to the physical quantity they represent)
What is a discrete-time signals and what is it represented by?
A signal that is defined and has a value at every instant of time within a given interval, represented by x(n)
What needs discrete-time signals?
Digital signal processing
Examples of Continuous Signals
- Sine Function
- Cosine Function
- Unit Step Function
- Rect Function
- Signum Function
- Practise in book
How is a discrete-time signal made?
By sampling a continuous-time
signal at equally spaced points in time t=kT
What does T in t=kT mean?
T is called the sampling period and a reciprocal of this value (fₛ)
is called the sampling frequency or sampling rate
fₛ = 1/T
How do we convert from continuous input to continuous output?
Continuous-time system transforms a continuous-time input x(t) to a continuous-time output y(t)
Physically it is realised using
analog circuits such as resistors, capacitors, inductors and amplifiers
How do we convert from discrete input to discrete output?
Discrete-time system transforms a discrete-time input x [k] discrete-time output y [k]
Physically a discrete-time system can be implemented in software or hardware using digital circuits
What process happen in ADC?
- Sampling
- Quantizing
In ADC how do digital singals work with values.
Digital circuits work with binary
signal which have only two discrete states, a logic “1” (HIGH) or a logic “0” (LOW).
Define Reference Voltage
Standard voltage against which
the analog input is measured
The reference voltage determines the range of the ADC and it varies among the devices
Define Analog Input Voltage
The input to be measured and
converted
The analog input Vin must be less than VRef to avoid
saturation of the ADC.
The analog inputs can be single-ended or differential.
What is resolution?
The number of bits required to represent each analog value.
Equation:
𝑉𝑅𝑒𝑓
2ᴺ
2ᴺ is the quantisation level
Why is having a high resolution important?
For an ideal ADC, the higher the resolution is the more higher of a chance that every possible analog input value will have
a unique digital output value
What may happen if the resolution is too high?
Unwanted signals may be picked up?
What is sampling?
The process in which the analog input data is sampled at regular
intervals so that an analog signal can be converted to a series of impulses representing the amplitude of the signal at a given instance
What is the sampling rate?
Frequency at which an analog signal is sampled
What is Shannon’s Theorem?
The minimum sampling
frequency should be at least twice the overall frequency or bandwidth of the signal to be measured, this is called Nqyuist rate
Equation for Nyquist Rate
fₛ ≥ 2fₘₐₓ
Where fₛ is the sampling frequency and fₘₐₓ is the maximum frequency of the input signal
How do we obtain a discrete-time signal by sampling?
By sampling a continuous-time
signal at equally spaced time instants, tn = nTs = n/fs
fs = 1/ Ts samples/sec
Ts is the fixed time interval between sampl
What is quantisation?
The process of assigning a binary value to the analog
sample
The sampled analog input will be replaced with an approximated finite set of discrete values.
