L02: Sinusoids and Frequencies Flashcards
What are the properties of a sinusoid?
- Amplitude
- Frequency
- Angular Frequency
- Period
- Phase (offset)
What does a Fast Fourier transform do?
The FFT algorithm is used to convert a digital signal (x) with length (N) from the time domain into a signal in the frequency domain (X)
What is a frequency component?
- A frequency component is a specific frequency or range of frequencies that make up a signal
- For example, if a sound is made up of multiple different frequencies, each of those frequencies could be considered a frequency component of the overall sound
What is a frequency filter?
Frequency filters process an image in the frequency domain, it is based on the FFT
When applying the filter, we multiply the filter by the spectrum
High pass frequency filters will allow high frequency components to go through
Low pass frequency filters will allow low frequency components to go through
What is a sinusoid?
- A sine curve
- An oscillating function, oscillates over 360 degrees
- Continues forever
What is the amplitude (A) of a wave and how do we calculate it?
Amplitude is the maximum displacement or distance moved by a point on a wave from the equilibrium position.
What is the angular frequency (ω) of a wave and how do we calculate it?
Angular displacement of any wave element per unit of time
ω = 2π/T = 2π x f
What is the bandwidth of a signal?
- The range of frequency components in a signal
- How much width it occupies in the frequency domain
What is the equation of a sinusoidal wave?
y(t) = A · sin(ω · t + θ)
What is the Fourier series?
- Any periodic signal s(t) may be represented as the sum of a set of sinusoidal waves of different frequencies and phases
- We can represent any signal as a combination of sinusoidal signals of different frequencies (and different amplitudes)
- The relative amplitudes of these different frequencies enables the signal to be modified by different amounts for each frequency
What is the frequency (f) of a wave and how do we calculate it?
The number of waves that pass in a given time period (1 second)
Measured in Hz
The frequency of a wave is the number of waves produced by a source each second. It is also the number of waves that pass a certain point each second. The unit of frequency is the hertz (Hz).
F = 1/T
What is the frequency domain?
- The frequency domain shows how much there is of a given signal
- Signals may be represented by frequency components
- Independent variable is frequency
What is the frequency range of standard human hearing?
20 Hz - 20 kHz
What is the period (T) of a wave and how do we calculate it?
The period is the time taken for a complete wave to pass through a particular point (measured in seconds), i.e. time taken to complete a whole wave
T = 1/F
What is the phase (θ) of a wave and how do we calculate it?
The offset of the wave
See how much the wave is shifted left/right
What is the shape of a high pass filter?
low to high
What is the shape of a low pass filter?
high to low
What is the spectrum of a signal?
- How a signal looks in the frequency domain= The signal’s spectrum
- Represents all the information of the signal (it is a mathematical transformation)
- From the spectrum we can get back all the signal in the time domain
What is the time domain?
- The real world happens in the time domain
- The independent variable is time
