Multimedia files like audio, video, and images are often very large in their uncompressed form. Compression is used to reduce the amount of data required to store or transmit this information, making storage more efficient and reducing bandwidth requirements for transmission. There are two main types of compression methods:

1. Lossless Compression: This preserves all the original data perfectly, meaning that the decompressed file is identical to the original. Examples include PNG for images and FLAC for audio.
2. Lossy Compression: This reduces the file size by removing less important or less noticeable data to human perception, often sacrificing some quality in the process. JPEG for images and MP3 for audio are popular lossy formats.

Lossy compression techniques are often used for audio, video, and images to remove data that is not perceptually significant to humans.

1. Human Perception Optimization: Lossy compression exploits limitations in the human eye and ear:
   1. For images, the human eye is less sensitive to subtle changes in high spatial frequency areas (fine details), which allows image compression methods like JPEG to reduce the size by dropping some fine-grained details.
   2. For audio, humans are more sensitive to lower frequencies and less sensitive to higher frequencies, which allows audio codecs like MP3 to selectively discard less audible frequencies.

When audio is recorded (e.g., with a microphone), it needs to be digitized for storage. The sampling rate is the number of times the audio signal is measured per second.

1. CD Quality Audio: Has a sampling rate of 44.1 kHz (44,100 samples per second), representing each sample as a 16-bit value. In stereo audio, two channels (left and right) are recorded, which means twice the amount of data is needed.
2. Example Calculation:
   1. 1 second of stereo CD quality audio:

\[ 44100 \text{ samples/second} \times 16 \text{ bits/sample} \times 2 \approx 1.4 \text{ Megabits} \] This is a significant amount of data for just one second of sound, demonstrating why compression is essential.

Video consists of a sequence of frames displayed rapidly to create the illusion of motion.

1. Full HD Video: A Full HD (1080p) frame has a resolution of 1920×1080 pixels, and with 24 bits per pixel (which allows for “true-color” with alpha transparency), one frame takes up:

\[ 1920 \times 1080 \times 24 \text{ bits} \approx 6 \text{ Megabytes} \]

1. A typical video displays 30 frames per second (fps), meaning that 240 MB of data would be required per second without compression. This is why video compression is vital to make streaming and storage practical.

The Fourier Transform is a mathematical operation transforming a signal from the time domain (or spatial domain, for images) to the frequency domain.

1. In multimedia compression, 2D Fourier Transform is used for images. It converts image pixels into frequency components. These frequency components can then be analyzed, and parts less significant to human perception can be discarded.
2. Example: Imagine an audio waveform where the amplitude is plotted over time. The Fourier Transform decomposes this waveform into its frequency components — figuring out which notes (frequencies) are being played and how loud they are. This concept is applied to images as well, allowing more effective compression.

1. In practice, this means that areas of an image with high-frequency details (e.g., fine patterns) can be simplified or removed during compression without significantly impacting the perceived quality. This is what is exploited in compression standards like JPEG to achieve significant size reduction.

The analogy mentioned in the text compares the Fourier Transform to recognizing musical notes in an audio recording:

1. Imagine you have a mono recording of music with different notes being played over time. The Fourier Transform is like figuring out which notes are being played (e.g., C#, C) during different time intervals.
2. This is similar to trying to write the musical score (sheet music) just by listening to the audio. By focusing only on the most important notes (the note heads), you would end up with a much more compressed version of the original sound while retaining most vital information.

1. Vision: The human eye is more sensitive to low spatial frequencies (smooth gradients) and less sensitive to high spatial frequencies (fine details or noise). This property is used in image and video compression to drop unnecessary detail in complex patterns, which most viewers won’t notice.
2. Hearing: The human ear is more sensitive to certain frequency ranges. MP3 compression uses this by discarding audio data in ranges we typically cannot hear well.

Multimedia compression methods, particularly lossy ones, take advantage of human sensory limitations to reduce data size without noticeable loss in quality. Techniques such as Fourier Transform allow multimedia compression algorithms to identify and remove less perceptible data, thereby achieving substantial compression ratios. These methods enable storing and transmitting multimedia content effectively, without overwhelming data storage capacities or requiring impractical bandwidth.