What is the Fourier Series?
The Fourier Series is a way to represent a periodic function as a sum of sine and cosine waves.
- It breaks down complex periodic signals into simpler trigonometric components.
- Each term in the series has a specific frequency, amplitude, and phase.
- Used in signal processing, physics, and engineering to analyse waveforms.
What are the key steps in analysis?
What is the difference between analogue and digital video?
Analogue video → uses continuous signals (like VHS tapes). Quality drops with noise or copying.
Digital video → uses binary data (0s and 1s). Quality stays consistent, easy to edit, supports HD/4K/8K.
What is a sinusoid?
A sinusoid is a smooth, repetitive wave that describes the shape of sine or cosine functions.
- It oscillates between a maximum and minimum value.
- Commonly used to model periodic phenomena like sound waves, light waves, and alternating current.
- Defined by its amplitude, frequency, phase, and offset
What is frequency?
f = 1/T
- how many cycles per second.
- T is the time taken to complete one wave cycle
What is phase (theta)?
Essentially how much the wave moves left or right. If theta = 0, the wave has not moved.
Generally an exam question will not be in context of a phase shift.
What is the equation of a sinusoid?
𝑦 (𝑡) = 𝐴 ∙ sin(𝜔 ∙ 𝑡 + 𝜃)
A = amplitude
T = time for one wave completion
f = frequency = 1/T
𝜔= angular frequency= 2𝜋f= 2𝜋/T
𝜃 = phase difference
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.
- any signal can be described as the
sum of sinusoidal waves of different frequencies.
What is the highest an analog transmission system will transmit?
450Hz.
What is the maximum of a digital transmission system bit rate?
4kbps, 8bit samples
What is the frequency domain?
The frequency domain is a way of analysing signals based on the frequencies they contain, rather than how they change over time.
- Transforms time-based signals into frequency components using tools like the Fourier Transform.
- Reveals how much of each frequency is present in a signal.
What is the Fast Fourier Transform (FFT)?
The FFT is an efficient algorithm to compute the Discrete Fourier Transform (DFT) of a signal.
- Converts a signal from the time domain to the frequency domain.
- Reveals the frequency components present in a discrete signal.
- Reduces computational complexity from O(n^2) to O(n \log n), making it ideal for real-time processing.
What are some applications of FFT?
Where does the square shape of a square wave come from?
The summation of many frequencies.
What is the spectrum of a signal?
What is the difference between the Fourier Series and Fourier Transform?
The Fourier series is used to represent a periodic function by a discrete sum of complex exponentials, while the Fourier
transform is then used to represent a general, nonperiodic function by a continuous superposition or integral of complex exponentials.
What is a low-pass filter?
A low-pass filter allows low-frequency signals to pass through while attenuating high-frequency signals.
- Smooths out rapid changes or high-frequency noise.
- Used in audio to reduce hiss or sharp sounds.
- Essential in data smoothing and anti-aliasing in graphics.
What is frequency filtering?
Frequency filtering is the process of modifying or removing specific frequency components from a signal.
Types of Filters:
- Low-pass: Keeps low frequencies, removes high.
- High-pass: Keeps high frequencies, removes low.
- Band-pass: Keeps a specific range of frequencies.
- Band-stop (notch): Removes a specific range of frequencies.
What is a high-pass filter?
A high-pass filter allows high-frequency signals to pass through while attenuating (reducing) low-frequency signals.
- Removes slow or low-frequency components (e.g., background hum).
- Used in audio processing to eliminate bass or rumble.
- Common in electronics, signal processing, and image enhancement.
A signal is only the variation of one variable (e.g., voltage) in time.
A. Yes
B. No
C. I don’t know
B. No
If you know the frequency of a signal, you also know its angular frequency and its period.
A. Yes
B. No
C. I don’t know
A. Yes
A sinusoidal signal is completely characterized by its amplitude and frequency.
A. Yes
B. No
C. I don’t know
B. No
A Fourier Transform is an alternative way to represent a signal.
A. Yes
B. No
C. I don’t know
A. Yes
Electromagnetic radiation with wavelengths between 400nm and 700nm is known as?
Visible light /visible spectrum (400nm is the top visible frequency, frequency decreases with wavelength)