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Westbay Waveform Master
Westbay Waveform Master is a brand new program, offering harmonic analysis of a wide range of waveforms. A set of parametrically defined standard waveforms is provided, along with a Custom Defined Waveform facility, and the ability to import waveforms from CSV and BMP files.
Graphical output includes spectral plots of Fourier Harmonics, and time domain plots of waveforms reconstituted from harmonics. Frequency domain modifications can be made by a comprehensive set of filters, or by a set of Non-Linear Characteristics.
Overview
All periodic waveforms can be expressed as the sum of a series of sinewaves, whose frequencies are exact multiples, or harmonics, of the fundamental signal frequency. The method of analysis uses the Fourier Series.
These are many instances when it is desirable to understand the harmonic content of a particular waveform, including non-linear analysis, circuit frequency response issues, and in aspects of electromagnetic compatibility (emc).
Westbay Waveform Master provides ten 'standard' waveforms, including several variations on trapezoidal waves, a damped oscillating sinusoid, a decaying exponential, and a triangular wave. In addition, a waveform can be built from a series of segments, consisting for example of linear rise and fall, constant amplitudes, exponential rise and fall.
Spreadsheet files in CSV format, containing data in amplitude - time format can be imported, and waveforms reconstructed and split into constituent harmonics.
Similarly, a BMP file containing a picture of a waveform can be imported and analysed.
Frequency modifications can be applied and analysed in both frequency and time domains, using either idealised filters, or network filters in the form of passive electrical elements.
A Non-Linear Characteristic of customisable form can be applied to any waveform.
An example of a waveform analysis follows, followed by further details of the program facilities, and links to pages with detailed description of the facilities.
Example Analysis
The following Standard Waveform was analysed, and its first 250 harmonics plotted:
The Ringing Trapezoid had a 1MHz repetition frequency, 5ns rise and fall times, and a 90ns ring period (11.11MHz). Its Fourier Harmonics are shown below.
The first harmonic shown represents the 1MHz fundamental. Note the second peak at the 11.11MHz ringing frequency.
Program Facilities
For additional information, follow the sub-heading link.
Simple trapezoidal, ringing trapezoidal,
damped rise and fall trapezoid, trapezoid with
overshoot.
Oscillating damped sinusoid, chopped
sinusoid, fractional sinusoid, rectified sinusoid, pure
sinewave.
Decaying exponential, triangular wave.
All waveform parameters independently definable. Up to five models of each waveform independently definable. The number of harmonics to be calculated is not limited. Root Mean Square and Mean Square (Power) values calculated for all waveforms.
A pulse train consisting of up to 50 high and low periods can be defined, using the form shown below:
Up to five independent models can be created, and RMS and Mean Square values are calculated during plotting.
Custom waveforms can be built using a series of up to 50 segments, consisting of linear rise and fall, constant amplitude, exponential rise and fall, fractional sinusoid and oscillating sinusoid forms.
Waveforms defined in spreadsheet files as a series of time and amplitude data pairs can be imported in Comma Separated Value (CSV) format. The imported waveform is analysed as a series of linear sections.
Pictures of waveforms saved in bitmap file format can be imported, and are then analysed as a series of linear sections.
Waveform Modifications
Three types of modification can be
performed on a waveform.
Basic
Filters - idealised filters in low-pass, high-pass, band-pass
and band-stop characteristics, with definable cut-off rates.
Network
Filters - passive element models of up to 11 stages, using
capacitors, inductors and resistors.
Non-Linear
Characteristics - three types of non-linear response can be
applied to any waveform, and the subsequent waveshape subjected to Fourier
Analysis.
Other Facilities
The product of two waveforms (of equal period) can be formed, to represent for example a power waveform. The fourier harmonics of the product can be viewed, and the linear product waveform also displayed.
Fourier harmonics can be exported to a CSV file.
Waveforms can be synthesised by direct entry of harmonic magnitude and phase values.