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Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....

Linear Approximation in Time Domain

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...

Active Filters

Active Filters

Active filters are electronic circuits that use operational amplifiers (op-amps), resistors, and capacitors to filter out unwanted frequency components from a signal. A first-order low-pass active filter is designed to pass signals with a frequency lower than a certain cutoff frequency and attenuate frequencies higher than that cutoff frequency. The transfer function for a first-order low-pass active filter is:

Op Amp AC Circuits

Op Amp AC Circuits

Within an audio system, the filter circuit plays a pivotal role in processing the amplified audio signal from an amplifier. Its primary function is significantly attenuating signal components with lower frequencies, thereby shaping the audio output. This circuit's operations are examined, focusing on the fundamental filter configuration. This configuration involves an operational amplifier arranged in an inverting setup coupled with resistors (R1 and R2) and a capacitor (C1).

Design Example: Capacitance Multiplier Circuit

Design Example: Capacitance Multiplier Circuit

In integrated circuit technology, a capacitance multiplier is often utilized to produce a larger capacitance value when a small physical capacitance falls short. This is achieved by a circuit that multiplies capacitance values by a factor of up to 1000, such that a 10-pF capacitor can replicate the performance of a 100-nF capacitor.
The circuit illustrated in Figure 1 below incorporates two op-amps, with the first operating as a voltage follower and the second acting as an inverting amplifier.

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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Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

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On the Design of an Energy Efficient Digital IIR A-Weighting Filter Using Approximate Multiplication.

Ratko Pilipović¹, Vladimir Risojević², Patricio Bulić¹

¹Faculty of Computer and Information Science, University of Ljubljana, 1000 Ljubljana, Slovenia.

Sensors (Basel, Switzerland)

|January 27, 2021

Summary

This study introduces a low-power digital A-weighting filter using approximate multiplication, achieving significant energy reduction with minimal impact on frequency response accuracy for noise measurement.

Keywords:

A-weighting filter approximate computing approximate filter band-pass digital filters noise sensing

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Area of Science:

Digital Signal Processing
Low-Power Integrated Circuit Design

Background:

A-weighting filters are crucial for environmental noise measurement.
Traditional implementations can be power-intensive, limiting portable applications.

Purpose of the Study:

To design a low-power digital A-weighting filter.
To evaluate the efficacy of approximate multiplication in reducing power consumption.

Main Methods:

Designed a sixth-order Infinite Impulse Response (IIR) filter.
Employed approximate odd radix-4 multipliers.
Analyzed effects of quantization and filter topology.
Synthesized using Verilog and Nangate45 cell library.

Main Results:

Achieved nearly 70% reduction in energy (power-delay product).
Demonstrated negligible deviation in frequency response compared to floating-point designs.
Verified performance through MATLAB simulations and synthesis.

Conclusions:

The proposed approximate multiplication approach enables highly energy-efficient digital A-weighting filters.
The design is suitable for environmental noise measurement applications without performance degradation.