Define a analogue signal & a digital signal
Analogue: a continuous waveform which is smooth and can range from any value e.g., blood pressure waveform
Digital: uses discrete and discontinuous values, represented as numbers which are specific. the digital values are sampled at regular intervals. e.g., audio recordings
Waveform is not smooth, static
Describe the advantages and disadvantages of analogue signal
ADV: continuous and smooth which reflects natural real-world signal accurately. Small input changes only cause small output changes. Circuits are fast and easy to implement. Analogue signals are resistant to aliasing.
DISADV: Susceptible to noise which can be directly added to the signal and cannot be removed, resulting in permanent distortion. Copying the signal reduces the quality and adds more noise each time.
- Analogue signals are hard to store
- Less flexible unable to compress, encrypt and needs complex circuitry for deep analysis
Describe the advantages and disadvantages of digital signal
ADV: Highly resistants to noise, values is unchanged unless threshold value is reached.
Can be copied without loss of quality and do not degrade with time. Cheap and easily stored
Digitals signals can be filtered, amplified and compressed. Greater depth to analysis and easy to integrate with other computer systems
DISADV: It requires a greater sample and number of channels. Processing can introduce time delays. If the sample frequency is too low aliasing occurs, the signal frequency is misinterpreted (must obey Nyquist limit). Information is lost due to sampling or quantization error
Describe the process of digitization (computer acquisition) of an analogue signal
- Sample discretion:
Analogue signal sampled at regualar intervals, produces voltage samples, to represent the signal the the sampling frequency must be at least twice the highest frequency present in the signal, in accordance with Nyquist limit - Quantization:
Each sampled voltage is rounded to the nearest available digital level. The number of available levels depends on the number of bits used per sample. - Each quantized value is converted into a binary number (a series of 0s and 1s). Each digit is called a bit
Describe the key outcomes of digitization
The original analogue signal becomes a series of numbers.
Accuracy depends on:
1. Sampling frequency
2. Number of bits per sample
3. Higher accuracy requires more storage and processing power.
Define binary
Binary encoding represents information using only 2 digits of 0 & 1.
Images and sounds are sequences of bits. 8 bits make a byte. The more bits the better the quality of a signal.
These binary values can be:
1. Stored in memory
2. Transmitted
3. Processed using digital signal processing techniques
The lowest number represented as a bit is 0000 & the highest is 1111, a 4 bit number has 16 different combinations.
In a byte the lowest number is 00000000 & the highest number is 11111111, with a total of 256 different combinations.
Define sampling
Sampling: where measuring the signal at regular time intervals. Each measurement = one sample. If sampling is too slow:
Signal appears at the wrong frequency. Important features may be missed. The shape of the waveform is distorted
This is not quantisation error — it’s a sampling problem.
Describe sampling rate/frequency
The number of samples taken per second (Hz) of an analogue signal which is measured when it is digitised. It has a major effect on how accurately the digital signal represents the original analogue signal.
Describe the effect of a high sampling rate and a low sampling rate
High: Many samples are taken per second
- The digital signal closely matches the analogue waveform
- Signal shape and frequency are accurately preserved
- Reduces the risk of sampling error (aliasing)
Result: High-quality, accurate digital signal
Low: Too few samples are taken per second
- Important parts of the waveform are missed
- The digital signal may appear to have:
- The wrong shape
- A lower or incorrect frequency
- This leads to sampling error, also known as aliasing.
Result: Distorted and inaccurate digital signal
Describe the relationship between storage and sampling rate/frequency
Sampling rate determines how many samples are taken per second
Higher sampling rate → more samples → more data
Effect on storage:
1. Storage is directly proportional to sampling rate
Example:
- 1000 samples/sec uses twice the storage of 500 samples/sec
📌 Higher sampling rate → more storage required
Describe sampling error
The error introduced when a continuous analogue signal is measured at discrete time intervals, causing the digitised signal to inaccurately represent the original signal if the sampling frequency is too low. Too few samples result in missing important parts of the waveform resulting in the reconstruction of the signal not matching the original analogue signal.
Caused by sampling in time, not by voltage rounding
Occurs when the sample rate is insufficient
Leads to:
1. Distortion of the waveform
2. Incorrect frequency (aliasing)
3. Different from quantisation error, which is due to limited voltage resolution
Define quantisation & quantisation error
Quantisation: in which a sample voltage is rounded to the nearest available digital value by a computer.
Quantisation error: Quantisation error is the maximum difference between the true analogue value and the nearest digital value. Impact of quantisation error:
1. Causes loss of accuracy
2. Appears as a “blocky” signal
3. Worse with fewer bits
Describe the relationship between quantisation error and storage
Relationship: Quantisation error decreases as the number of bits per sample increases
More bits → more possible voltage levels → smaller error
Effect on storage:
1. Each extra bit increases the data size
2. Doubling the bits doubles the storage required
Example:
8-bit sample = 1 byte
16-bit sample = 2 bytes
📌 Lower quantisation error → more storage required
Describe the relationship between number of channels and storage
Each channel is stored independently. Multi-channel systems record multiple signals simultaneously
Effect on storage:
1. Storage increases linearly with the number of channels
Example:
2 channels require twice the storage of 1 channel
3 channels require three times the storage of 1 channel
📌 More channels → more storage required
Define the nyquist limit
The minimum sampling frequency needed to accurately digitize a signal, must be at least 2x the highest frequency present in the signal.
Important as sampling below the Nyquist limit results in aliasing, which makes high frequency signals appear as low frequency signals, once aliasing occurs the original signal cannot be recovered.
For an ECG a min of 300 samples required, good quality ECG requires 1000+
Describe the Nyquist limit equation
f sample- frequency sample
f max- highest frequency component of a signal
f sample ≥ 2 x f max
Define aliasing
Aliasing is a form of sampling error that occurs when an analogue signal is sampled at a rate below the Nyquist limit, causing the digitised signal to appear at an incorrect (usually lower) frequency.
Occurs as: The signal contains frequency components higher than half the sampling frequency
- The sampling process misinterprets these high-frequency components
EFFECT: Incorrect waveform shape
- Wrong frequency representation
- Loss of clinically or scientifically important information
- The original signal cannot be recovered
Describe effect of aliasing on an ECG
Fast events (pacing spikes, sharp QRS complexes) may:
1. Appear smaller
2. Appear slower
3. Be missed entirely
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Introduction7
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Accuracy & precision10
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Week 3: signal processing22
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Week 4: physics of pressure & flow, BP measurement37
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Week 5: Echocardiography31
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Week 6: Ohms law & circuits16
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Week 7: Clinical applications of Ohms law27
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Week 8: Alternating current22
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Week 9: Amplification26
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Week 10A: electrical safety23
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Week 10B: Filters21
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Week 11: Computer acquisition18
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Week 12: ECG measurement & radiation22
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Week 13: Medical imaging27
