2. Signals Flashcards
What is a signal’s amplitude, phase, frequency and period mathematically?
- Frequency (Hz) is the number of identical patterns (cycles) contained in one second; signal of 10 Hz performs 10 cycles each second
- Period is the length of time interval (seconds)
- Amplitude is the height from the centre line to the peak
- Phase is the time it takes to complete one cycle
What is spatial resolution and colour resolution in a sampled digital image?
Spatial sampling converts image into a 2D structure where brightness is known only at discrete points in space (= pixels)
- Spatial resolution of image is M x N
- M = image size (number of pixels) in the horizontal direction
- N = image size in the vertical direction
- High spatial resolution = large number of pixels are used = finer details in image
Colour resolution is the number of bits necessary to represent the colour of a pixel
- Higher colour resolution = higher colour quality
What are the different types of images?
A digital 2D image is represented by a 2D discrete-space, discrete-color function that assigns to each pixel a color
- Stored in the computer as a two-dimensional array p where each element of the array stores the color of the pixel situated in position (x,y)
- Color is a finite-precision integer number
How are types of images represented in a computer?
Binary (B&W)
- Black-and-white images, pixels are either 0 or 1
- Color res = 1 bit
- 100x100 image only needs 100x100 bits
Greyscale
- Each color is a shade of grey, from 0 (black) to 255 (white)
- Color res = 8 bits
- 100x100 image needs 100x100x8 bits
True color (RGB)
- Each pixel has a color described by amount of red, green, and blue in it
- Each color is a value in the range 0-255
- (0,0,0) is black
- (255,0,0) is red
- (255,255,255) is white
- Represented with three MxN arrays, one for each RGB color:
p[x,y]=[R(x,y), G(x,y), B(x,y)]
- Color res = 3x8 = 24 bits
- 100x100 image needs 100x100x24 bits
What is sampling?
Sampling - measures the signal’s level and produces a finite-length sequence of samples / the process of measuring a continuous signal at isolated, equally spaced moments in time.
Computer does not have enough time or space to record every continuous signal at every single moment so it instead records signals at a set pace
The result is a discrete-time representation of the continuous input signal as a sequence of samples.
What is an ADC? and how does it work?
The analog-to-digital converter (ADC) is the tool used to undergo digitization; the process by which signals are processed into information that the computer can work with.
Two stages of digitization:
Sampling - measures the signal’s level and produces a finite-length sequence of samples
Quantization - converts samples into a sequence of finite-precision numbers
ADC has 2 analog inputs (Vin and Vref) and few digital outputs
- Vin is the voltage to be digitized
- Vref is the constant reference voltage that will define the input range
- Example: ADC with Vref = 8 V can measure voltages in range 0-8 V - N output pins are used to encode the result of digitization
How does the ADC work?
- Samples the analog continuous input voltage and obtains Vin
- Compares instantaneous Vin reading to the reference voltage Vref and quantifies their ratio
- ADC generates digital output
What is a DAC?
The digital-to-analog converter (DAC) is the tool used to undergo reconstruction to reassembling an analog signal from its digital samples; the reverse of digitization to decipher the carried message and send signals back to the real world.
What is sampling frequency?
Sampling frequency is the number of samples taken every second:
Fs = 1/Ts
where Ts = sampling period (sec)
What is sampling period? how high does the frequency need to be?
Sampling period is the distance in time between two successive sampling moments.
Depends on the type of system (ex: smart home can measure room temperature once/min but safety critical system like airbag control system should measure car’s acceleration 100 times/sec)
What is Shannon’s theorem? what happens if we do not obey Shannon’s theorem?
Shannon sampling theorem says that the sampling period should not be greater than 1/2 of the finest detail in the signal; sampling frequency has to be at least twice the maximum frequency in the signal
What is undersampling, oversampling and aliasing?
Oversampling happens when sampling with a higher rate than the Nyquist rate. - Oversampling will improve the reconstructed waveform but also takes up more storage and computational needs of the system
- Tradeoff between sampling frequency and system capacity
Aliasing is the effect of under-sampling: Alias frequencies are the false frequencies resulted after reconstruction
