Package wiat :: Package TM :: Module Inst

Module Inst

Inst.py - This file contains the class defining an Instrument and the functions CalculateImpedance and CalculateMaxima.

The CalculateImpedance returns the impedance of an instrument for each requested frequency.

The CalculateMaxima seach for the exact location of the maxima of the instrument and return a list of (frequency,magnitude) tuples.

Classes

[hide private]

Instrument
Class used to descibed the geometry of a musical instrument.

Functions

[hide private]

create_identity_matrix_array(n)
Returns an array of 2X2 identity matrices for uses in the transmission matrix calculation method.

source code

multiply_matrix_arrays(TM1, TM2)
Multiplication of two arrays of 2X2 matrices.

source code

CalculateImpedance(instrument, freqs, T=25.0)
Calculate the input impedance of the instrument.

source code

CalculateMaxima(Z, inst, freqs, T, number_of_maxima=None)
Calculate the exact location of the impedance maxima of an Instrument.

source code

Function Details

[hide private]

multiply_matrix_arrays(TM1, TM2)

source code

Multiplication of two arrays of 2X2 matrices.

Example:

>>> TM1 = create_identity_matrix_array(10)
>>> TM2 = multiply_matrix_arrays(TM1,TM1)
>>> TM1 == TM2
array([[[ True,  True,  True,  True,  True,  True,  True,  True,  True,
          True],
        [ True,  True,  True,  True,  True,  True,  True,  True,  True,
          True]],
<BLANKLINE>
       [[ True,  True,  True,  True,  True,  True,  True,  True,  True,
          True],
        [ True,  True,  True,  True,  True,  True,  True,  True,  True,
          True]]], dtype=bool)
>>>

CalculateImpedance(instrument, freqs, T=25.0)

source code

Calculate the input impedance of the instrument.

This function performs the transfer matrix multiplication.

The frequency vector f must be sufficiently fine for the impedance to be well represented, otherwise, the CalculateMaxima functions won't be able to find the maxima. A good vector is:

>>> freqs = numpy.arange(50,5000,5,dtype=float)

Parameters:

instrument - an Instrument instance
freqs - frequency vector
T - the temperature

CalculateMaxima(Z, inst, freqs, T, number_of_maxima=None)

source code

Calculate the exact location of the impedance maxima of an Instrument.

It uses an impedance vector Z, previously calculated with the CalculateImpedance function, to determine the approximate location of the maxima and then, uses an optimization algorithm to find their exact location.

Parameters:

Z - impedance vector
inst - Instrument instance
freqs - frequency vector
T - temperature
number_of_maxima - optional argument to limit the number of maxima that are returned

Returns:

a list of tuples containing frequency and magnitude of each impedance maxima.