Fourier Transform Explanation Flashcards
(20 cards)
What is the purpose of Fourier Transform (FT) in multimedia applications?
To transform signals to the frequency domain
FT shows how much of each frequency is in a signal/image.
Which type of Fourier-related transform is commonly used in MP3 audio compression?
Modified Discrete Cosine Transform (MDCT)
Used in MP3 compression for efficient time-frequency representation.
What happens if a signal is sampled below its Nyquist frequency?
Aliasing occurs
Sampling below Nyquist rate creates false low frequencies (aliasing).
What property of the Fourier Transform states that convolving two signals is equivalent to multiplying their Fourier spectra?
Convolution theorem
Convolution in time = multiplication in frequency (and vice versa).
Which part of a Fourier Transform result is most important for spatial information in an image?
Phase Spectrum
Phase holds spatial detail — without it, images lose structure.
In 2D Fourier Transform, high frequencies correspond to:
Sharp edges and fine details
High frequencies carry rapid changes in pixel intensity.
In Fourier Transform terms, smoothing an image with a Gaussian filter corresponds to:
Multiplying by a low-pass filter in frequency domain
Gaussian blur removes high frequencies, acting like a low-pass filter.
The Discrete Cosine Transform (DCT) differs from DFT primarily because:
It operates on real-valued signals and uses only cosines
DCT avoids complex numbers and is better for image compression.
Why do we apply log transformation to Fourier spectrum visualizations?
To compress dynamic range and make small components visible
Spectrum values vary greatly; log scale helps visualization.
What domain is preferred for real-time convolution operations?
Frequency domain
Convolution in frequency space is faster via multiplication.
Which problems are associated with sampling and aliasing?
A. Loss of high-frequency information
B. Appearance of false low frequencies
C. Signal enhancement
D. Need for higher sampling rates
Loss of high-frequency information; Appearance of false low frequencies; Need for higher sampling rates
Aliasing distorts signals if not sampled correctly.
In image compression (e.g., JPEG), after DCT, what steps are applied?
A. Quantization
B. Zigzag ordering
C. Color balancing
D. Entropy coding
Quantization; Zigzag ordering; Entropy coding
JPEG compresses DCT data by reducing detail, reordering it, and applying lossless compression.
Which applications involve Fourier Transform in audio processing?
A. Noise reduction
B. Speech recognition
C. Image deblurring
D. MP3 compression
Noise reduction; Speech recognition; MP3 compression
Fourier analysis supports signal separation and compression.
Properties of Fourier Transform include:
A. Linearity
B. Symmetry for real-valued functions
C. Non-periodicity
D. Similarity theorem
Linearity; Symmetry for real-valued functions; Similarity theorem
FT properties enable efficient signal processing.
Effects of applying Gaussian smoothing in the frequency domain include:
A. Reduction of high-frequency components
B. Enhancement of sharp edges
C. Low-pass filtering
D. Noise suppression
Reduction of high-frequency components; Low-pass filtering; Noise suppression
Gaussian smoothing reduces detail and noise.
In 2D-DFT, high frequencies:
A. Are located farther from the center
B. Represent fine details
C. Represent average color
D. Can be visualized along horizontal and vertical axes
Are located farther from the center; Represent fine details; Can be visualized along horizontal and vertical axes
Center = low freq, outer = fine details in DFT.
In Fourier Transform applications to CNNs and deep learning, FFT is used to:
A. Accelerate convolution operations
B. Perform dimensionality reduction
C. Speed up training
D. Enhance activation functions
Accelerate convolution operations
FFT allows convolution to be done as multiplication.
Fourier Transform helps in augmented and virtual reality (AR/VR) by:
A. Real-time filtering of images
B. Spatial audio rendering
C. Gesture recognition
D. Increasing network bandwidth
Real-time filtering of images; Spatial audio rendering; Gesture recognition
FT is used in audio/video filtering and signal recognition.
Inverse filtering in imaging aims to:
A. Smooth the image
B. Undo blurring effects
C. Recover original signals
D. Enhance edges
Undo blurring effects; Recover original signals
Inverse filters try to reconstruct the original input.
The FFT (Fast Fourier Transform) is important because:
A. It reduces computation time
B. It is more accurate
C. It uses fewer samples
D. It allows real-time applications
It reduces computation time; It allows real-time applications
FFT is optimized for speed — enabling live processing.
