ADCs and Filters Flashcards
Steps of digital signal processing (DSP)
- Physical stimulus
- Capture analogue signal using sensors or transducers
- Filter and amplify signal to prep for digitisation
- Sampling - ADC converts the continuous-time signal as discrete-time samples
- Quantisation (ADC detects voltage steps) - resolution is determined by dividing the amplitude range into discrete levels (i.e discrete amplitude values are assigned to the sampled signal to produce a digital presentation)
- Digital processing - applying digital filters to fine tune the signal
- Signal is stored
Sampling
Takes the continuous analogue signal and measures it at set intervals, capturing discrete points
Sampling rate/frequency (Fs)
Frequency/number of samples taken per second, the speed at which the ADC captures the data, measured in Hz
Higher Fs → more detail captured from the analogue signal
Based on the Nyquist Theorem, it should be at least twice the maximum frequency of the signal to avoid aliasing
Fs = 1 / Ts
Sampling time (Ts)
Set time/interval between each sample taken
Smaller Ts → more samples per second → more accurate signal that best represents the original
Represented along x-axis
Quantisation
After sampling is complete, the ADC divides the entire voltage range, from minimum to maximum voltage, into discrete steps (voltage steps), with each step representing a specific value.
n = 2m; where n = voltage steps and m = number of bits (resolution)
More bits = finer resolution (digital resolution is finite as it uses binary, analogue is infinite as it can be any possible value)
∆V
Smallest change/difference in the input analogue signal that causes a change to the digital output. It is the step sizes between quantisation levels.
Depends on the total voltage range of the input signal and the resolution.
More steps there are (the higher n is) → the finer the ADC can detect small changes in voltage
∆V = Voltage Range / 2n
Where voltage range = max. voltage - min. voltage
Voltage Resolution (Vres)
Represents the smallest change in voltage (voltage step) that the ADC can resolve.
It depends on the reference voltage (Vref) and the number of bits
Smaller Vres → higher precision
Vres = Vref / 2n
Reference Voltage (Vref)
The maximum voltage that the ADC can measure and convert to a digital value
It defines the voltage range, typically from 0 to Vref
Represented at top of y-axis
Completely determined signal in ADC
A signal that was sampled in a way that all its info can be fully captured and reconstructed from the digital representation i.e the sampling and digitisation process has preserved all the essential info from the original analogue signal i.e the new digital signal still resembles the original analogue signal.
Dependent on:
1. If it was sampled at twice the rate of the highest frequency in the signal to avoid aliasing
2. If it was converted from continuous to discrete with sufficient resolution (high number of bits results in fewer errors and finer outputs with preserved info)
3. If the original analogue signal was free from noise and distortion
What is the accuracy of ADC dependent on?
Sampling frequency (Fs) and resolution (number of bits, m)
What must the sampling rate be in order to capture all the frequencies in the signal?
Twice the highest frequency of the signal
i.e if the V res is 500Hz, the Fs must be 1000Hz
Nyquist Frequency/Limit
To accurately capture a continuous signal without aliasing, the sampling frequency must be at least twice that of the highest frequency of the anaolgue signal.
If the signal is sufficiently high, it will result in the signal being captured without the loss of important details.
If the signal is too low, it will result in loss of critical details about the signal and aliasing will occur.
Fs ≥ 2 x Fm
Fourier Series
A way of breaking down complex signals, like waveforms, into simpler components, like sine waves.
So any signal, no matter how complex, can be represented as a combination/sum of these simpler sine waves with different frequencies.
The more sine waves used → the more accurately the complex signal can be represented.
Anti-aliasing filters
Prevent high frequency components that could cause aliasing from entering the ADC. So a low pass filter would be used before digitisation as well as applying the Nyquist theorem to ensure accurate, alias-free signal processing
Phase Delay
