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Reconstruction of Signal using Interpolation

Reconstruction of Signal using Interpolation

Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next...

Aliasing

Aliasing

Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original...

Upsampling

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...

Bandpass Sampling

Bandpass Sampling

In signal processing, bandpass sampling is an effective technique for sampling signals that have most of their energy concentrated within a narrow frequency band. This type of signal is known as a bandpass signal. The key principle of bandpass sampling involves sampling the signal at a rate that is greater than twice the signal's bandwidth to prevent aliasing.
A bandpass signal has a spectrum with a lower frequency limit, denoted as ω1, and an upper frequency limit, denoted as ω2....

Sampling Theorem

Sampling Theorem

In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.

Design Example

Design Example

The innovation of touch-tone telephony revolutionized the telecommunications industry by replacing the traditional rotary dial with a dual-tone multi-frequency (DTMF) signaling system. This system uses a matrix-style keypad with buttons arranged in four rows and three columns, creating 12 distinct signals each assigned to a pair of frequencies. Each button press results in a simultaneous generation of two sinusoidal tones – one from a low-frequency group (697 to 941 Hz) and one from a...

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Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans

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Information Bottleneck Signal Processing and Learning to Maximize Relevant Information for Communication Receivers.

Jan Lewandowsky¹, Gerhard Bauch², Maximilian Stark²

¹Fraunhofer Institute for Communication, Information Processing and Ergonomics, Fraunhoferstraße 20, 53343 Wachtberg, Germany.

Entropy (Basel, Switzerland)

|July 27, 2022

Summary

Digital communication receivers can be simplified using the information bottleneck method. This approach maximizes relevant information flow while reducing processing complexity for efficient signal processing.

Keywords:

information bottleneck machine learning mutual information

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Area of Science:

Digital communication
Information theory
Signal processing

Background:

Digital receiver signal processing is complex, leading to power, delay, and chip area bottlenecks.
High precision (many bits per sample) and demanding arithmetic operations increase hardware complexity.
Recent trends focus on information theory for designing receiver chains and building blocks.

Purpose of the Study:

To explain the fundamental similarities between the information bottleneck method and communication receiver functionalities.
To present and investigate new results on an entire receiver chain designed using the information bottleneck principle.
To provide an overview and analysis of information bottleneck signal processing techniques in the literature, particularly for channel decoding.

Main Methods:

Applying the information bottleneck principle to design signal processing blocks.
Maximizing the flow of relevant information through signal processing units.
Utilizing strong quantization to reduce the number of bits processed, thereby lowering complexity.
Analyzing similarities between different information bottleneck signal processing approaches.

Main Results:

Demonstrated an entire receiver chain designed based on the information bottleneck principle.
Presented new investigation results on this information bottleneck-designed receiver chain.
Offered a comparative analysis of various information bottleneck techniques from existing literature, focusing on channel decoding.

Conclusions:

The information bottleneck method offers a powerful framework for designing efficient digital communication receivers.
This approach allows for the creation of signal processing blocks with simpler mathematical operations.
A general view of information bottleneck signal processing emerges, relating to learning trainable functions that maximize mutual information under compression.