ECExplain

Contents

Signals & Systems
Signal Classification
Continuous Time SignalsDiscrete Time SignalsPeriodic SignalsAperiodic SignalsEven and Odd SignalsEnergy SignalsPower SignalsDeterministic vs Random SignalsReal and Complex Signals
Signal Operations
Unit Step FunctionUnit Impulse FunctionRamp SignalExponential SignalsSinusoidal SignalsSignum FunctionRectangular PulseTriangular PulseSinc FunctionTime ShiftingTime ScalingTime ReversalAmplitude ScalingSignal Addition and Multiplication
LTI Systems
System ClassificationLinearity TestTime Invariance TestImpulse ResponseConvolution IntegralConvolution PropertiesConvolution SumStep ResponseCausality from Impulse ResponseBIBO StabilityCascade and Parallel SystemsFeedback SystemsInvertibility
Fourier Series
Trigonometric Fourier SeriesExponential Fourier SeriesFourier Series SymmetryFourier Series of Square WaveFourier Series of Sawtooth WaveFourier Series of Triangle WaveFourier Series PropertiesGibbs PhenomenonPower Spectrum of Periodic Signals
Fourier Transform
Fourier Transform DefinitionInverse Fourier TransformFT of Rectangular PulseFT of Impulse FunctionFT of Exponential SignalFT of Signum FunctionFT of Step FunctionFT of Cosine and SineFourier Transform PropertiesTime Scaling Property FTConvolution Theorem FTMultiplication Property FTParseval TheoremHilbert Transform
Laplace Transform
Laplace Transform DefinitionRegion of ConvergenceLT of Standard SignalsLaplace Transform PropertiesInitial Value TheoremFinal Value TheoremInverse Laplace TransformInverse LT of Repeated PolesTransfer FunctionPole Zero Plot LaplaceSystem Analysis Using Laplace
Z-Transform
Z-Transform DefinitionZ-Transform ROCZ-Transform of Standard SequencesZ-Transform PropertiesInverse Z-TransformTransfer Function H(z)Stability from Z-Transform
Sampling & Reconstruction
Sampling TheoremAliasingIdeal ReconstructionPractical ReconstructionAnti-Aliasing FilterSampling of Discrete Time Signals
Other Topics
Other Subjects
Analog ElectronicsDigital ElectronicsControl SystemsElectromagnetic TheoryDigital CommunicationAnalog CommunicationNetwork AnalysisMicroprocessorsVLSI DesignVerilog HDLPower ElectronicsEmbedded SystemsDSPElectronic Devices
Section Progress93%

13 of 14 articles

Amplitude Scaling

a*x(t) amplification and attenuation.

Darshan N
Updated: 7 April 2026
7 min read

Amplitude scaling multiplies the signal height by a constant mathematical factor. Every electronic amplifier implements this basic mathematical operation to boost weak sensor readings.

x(t)2x(t)t
Amplitude scaling stretches the waveform vertically without altering timing.

Core Concept

This operation changes the physical strength of the signal. The horizontal timing of all events remains completely untouched. Only the vertical peaks and valleys stretch.

If the multiplier is greater than one, the signal experiences amplification. The waveform grows taller. This physically mimics turning up the volume on a stereo system.

If the multiplier falls between zero and one, the signal faces attenuation. The waveform shrinks vertically. A negative multiplier adds an upside down vertical flip.

Key Formula

The amplitude scaled signal is expressed as y(t) = A * x(t). The constant A dictates the strict gain or loss applied to the system.

Example
Given: A signal x(t) has a maximum value of 5 and a minimum of -2. Find the range of y(t) = -3 * x(t).\nFormula: Apply multiplier to the extremes and sort.\nSteps:\n1. Multiply the original maximum: -3 * 5 = -15.\n2. Multiply the original minimum: -3 * -2 = 6.\n3. The new maximum is 6.\n4. The new minimum is -15.\nFinal Answer: The scaled signal ranges vertically from -15 to 6.
Exam Tip: Amplitude scaling affects the physical energy of the signal by the square of the scaling factor. Do not simply multiply the energy by the base scalar.

Properties Summary

  • Amplification: Factor magnitude greater than 1 increases amplitude.
  • Attenuation: Factor magnitude less than 1 decreases amplitude.
  • Inversion: A negative scaling factor flips the signal across the time axis.
  • Linearty: The operation strictly obeys the classical superposition principle.
  • Energy scaling: If y(t) = A*x(t), then Energy of y equals A^2 times Energy of x.

Quick Revision

  • Stretches graph vertically.
  • Leaves horizontal time axis alone.
  • Used in ideal linear amplifiers.
  • Can invert the signal phase.
  • Squares the energy change factor.
  • Exam trap: Incorrectly applying the amplitude multiplier to the time variable limits during energy integration.
#Signals & Systems

Amplitude Scaling Quiz

Test your knowledge of amplitude scaling operations on signals.

Question 1 of 3

Q1.If x(t) has Fourier transform X(f), the Fourier transform of 5*x(t) is:

Related Articles

Time Scaling

x(at) compression and expansion, effect on frequency.

4 min read

Sinusoidal Signals

Amplitude, frequency, phase, representation forms.

12 min read

Ramp Signal

r(t) = t*u(t), relation to step function by integration.

9 min read

Time Scaling Property FT

x(at) <-> (1/|a|)F(w/a), bandwidth-duration tradeoff.

10 min read

Exponential Signals

Real and complex exponentials, growth and decay.

9 min read

Previous
Time Reversal
Next
Signal Addition and Multiplication