ASN FilterScript – Reference guide

ASN FilterScript scripting language supports over 82 scientific commands for DSP filter design. It provides designers with a familiar and powerful programming language for designing IIR/FIR digital filters with the most demanding technical specifications.

Trigonometrical functions

Function	Syntax	Description
`angle`	`y = angle(x)`	Compute the inverse tangent (four quadrant)
`cos`	`y = cos(x)`	Compute the cosine
`cosh`	`y = cosh(x)`	Compute the hyperbolic cosine
`sin`	`y = sin(x)`	Compute the sine
`sinh`	`y = sinh(x)`	Compute the hyperbolic sine
`tan`	`y = tan(x)`	Compute the tangent
`tanh`	`y = tanh(x)`	Compute the hyperbolic tangent

Vector functions

Function	Syntax	Description
`augmentpoly`	`y = augmentpoly(a,R)`	Creates a single polynomial from R identical polynomials. Where, \(Y(z)=\left[A(z)\right]^R \) for \(1\le\ R\ \le\ 10 \). Use this function for implementing Kolmogorov–Zurbenko (KZ) lowpass filters, and improving the sideband attenuation characteristics of an FIR filter. The function will automatically analyse the generated coefficients and remove any leading or trailing zeros.
`cols`	`y = cols(x)`	Gets number of columns in the vector x
`conv`	`y = conv(a,b)`	Computes the linear convolution of input vectors a and b. Where, the length of y is equal to `length(a) + length(b)-1`
`diff`	`y = diff(x)`	Gets the difference between adjacent values of the vector `x`
`eldef`	`A(3,0) = eldef(5)`	Sets the vector element value to the given value
`length`	`y = length(x)`	Gets the vector length
`max`	`y = max(x)`	Gets the maximum of the vector `x`
`mean`	`y = mean(x)`	Gets the mean of the vector `x`
`min`	`y = min(x)`	Gets the minimum of the vector `x`
`ones`	`y = ones(N)`	Vector of 1s of length `N`
`poly`	`y = poly(x)`	Convert roots to polynomial
`reverse`	`y = reverse(x)`	Flip vector elements up-to-down
`roots`	`y = roots(x)`	Get the roots of polynomial x
`rows`	`y = rows(x)`	Gets the number of rows in vector `x`
`series`	`y = series(min,step,max)`	Creates a data series
`sortup`	`y = sortup(x)`	Sort vector in ascending order: smallest first, largest last
`sortdown`	`y = sortdown(x)`	Sort vector in descending order: largest first, smallest last
`stddev`	`y = stddev(x)`	Gets the standard deviation of `x`
`sum`	`y = sum(x)`	Gets the sum of vector `x`
`transpose`	`y = transpose(x)`	Transpose vector `x`
`winfunc`	`y = winfunc(L,WinType, Beta)`	Returns L weighting coefficients for the Window method specified by `WinType`. The following window functions are supported: `rectangular, blackman, blackmanharris, hamming, hanning, flattop, kaiser` and `Chebyshev`. `Beta` is only required for `Chebyshev` and `kaiser` and should be `0` for all other functions.
`zeros`	`y = zeros(N)`	Vector of 0s of length `N`

General functions

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Function	Syntax	Description
`abs`	`y = abs(x)`	Compute the absolute value(s).
`ceil`	`y = ceil(x)`	Round up to infinity.
`conj`	`y = conj(x)`	Compute the complex conjugate.
`exp`	`y = exp(x)`	Compute the exponential of the argument, i.e. \(e^x \)
`pow2`	`y = pow2(x)`	Compute the element to the power of 2, i.e \(2^x\)
`pow10`	`y = pow10(x)`	Compute the element to the power of 10, i.e \(10^x\)
`flip`	`y = flip(x)`	Flip the real and imaginary components of `x`
`floor`	`y = floor(x)`	Round down to \( -\infty\)
`fft`	`y = fft(x)`	Fast Fourier transform. The input `x` must be a vector
`ifft`	`y = ifft(x)`	Inverse fast Fourier transform. The input `x` must be a vector
`imag`	`y = imag(x)`	Get the imaginary component of `x`
`ln`	`y = ln(x)`	Natural log of `x`
`log10`	`y = log10(x)`	Log base 10 of `x`
`log2`	`y = log2(x)`	Log base 2 of `x`
`logn`	`y = logn(N,x)`	Log of `x` to base `N` of `x`
`newpz`	`y = newpz(mag,freq)`	Define a root: \(0 \leq mag \leq 5\) and \( 0 \leq freq \leq \pm f_s/2\) \( \displaystyle roots =\) {\( \displaystyle (z-r_1 e^{-i \theta_1}), (z-r_2 e^{-i \theta_2}), …. \)} Where, \( \displaystyle \theta_x = \frac{2 \pi f}{f _s} \) Example [code lang=”java”] ClearH1; // clear primary filter from cascade interface fc = {45,55,.1,50}; // interface variable definition interface radius ={0.5,.999,0.01,0.97}; Main() Rts={newpz(1,fc),conj(newpz(1,fc)),newpz(1,2fc),conj(newpz(1,2fc)), newpz(1,3fc),conj(newpz(1,3fc))}; Num = {poly(Rts)}; // define numerator coefficients Den = {poly(Rts*radius)}; // define denominator coefficients Gain = sum(Den)/sum(Num); // define gain
`real`	`y = real(x)`	Get the real component of `x`
`round`	`y = round(x)`	Round `x`
`sqr`	`y = sqr(x)`	Square of `x`
`sqrt`	`y = sqrt(x)`	Square root of `x`

Math operators

Math Operators

Operator	Example syntax	Description
`+`	`a+b`	Addition.
`-`	`a-b`	Subtraction.
`*`	`A*B`	Multiplication.
`/`	`A/B`	Division.
`.*`	`A.*B`	Element-by-element vector multiplication.
`./`	`A./B`	Element-by-element vector division.
`.^`	`a.^N`	Element-by-element vector to the power.
`^`	`a^N`	Vector to the power.
`!`	`N!`	Factorial.

IIR filter design methods

A summary of all classical and specialist IIR filter design methods that are supported is given in this section.

FUNCTION	DESCRIPTION
`bessel`	Bessel filter
`butter`	Butterworth Filter
`cheby1`	Chebyshev I Filter
`cheby2`	Chebyshev II Filter
`ellip`	Elliptic Filter
`arbmagphase`	Arbitrary Response Magnitude and Phase Filter
`cplxfreqshift`	Complex Frequency Shift Transformation Filter
`dcremover`	DC Component Remover
`notch`	Notch Filter
`peaking`	Peaking/Bell Filter

Miscellaneous digital filter functions

FUNCTION	SYNTAX	DESCRIPTION
`augment`	`Hd=augment(Hd1,Hd2, DFormat)`	Augment or merge two digital filter objects, and return the merged objects as a single object in `Hd`
`computegain`	`G=computegain(Hd,Fo)`	Get the gain, `G` of the analog filter (Hd) at frequency point, `Fo`. Where, `Fo` is specified in same base unit as the sampling frequency, `Fs`, i.e. Hz, kHz etc
`getnum`	`Num = getnum(Hd)`	Get the numerator coefficients of analog filter object,`Hd`
`getden`	`Den = getden(Hd)`	Get the denominator coefficients of analog filter object, `Hd`
`getgain`	`G = getgain(Hd)`	Get the gain of analog filter object, `Hd`
`refspectrum`	`y = refspectrum(Hd)`	Sets the reference magnitude spectrum to, `Hd`

FIR filter design methods

A summary of all FIR filter design methods that are supported is given in this section.

FUNCTION	DESCRIPTION
`movaver`	Moving Average
`firwin`	FIR filter Window method
`firminphase`	FIR minimum phase filter
`firarb`	FIR arbitrary magnitude response filter
`firkaiser`	Kaiser window FIR filter
`firgauss`	Gaussian
`firlp2notch`	Linear notch filter
`savgolay`	Savitzky-Golay smoothing filter
`savgolaydiff`	Savitzky-Golay differentiation filter

Analog -> digital filter design: Laplace transforms

Laplace analog transfer functions may be entered and converted into their digital equivalents via the following commands:

FUNCTION	DESCRIPTION
`analogtf`	Analog Transfer Function
`bilinear`	Bilinear Transform
`mztrans`	Match Z-transform

miscellaneous analog filter design functions

FUNCTION	SYNTAX	DESCRIPTION
`augment`	`Ha=augment(Ha1,Ha2, DFormat)`	Augment or merge two analog filter objects, and return the merged objects as a single object in `Ha`
`computegain`	`G=computegain(Ha,Fo)`	Get the gain, `G` of the analog filter (Ha) at frequency point, `Fo`. Where, `Fo` is specified in same base unit as the sampling frequency, `Fs`, i.e. Hz, kHz etc
`getnum`	`Num = getnum(Ha)`	Get the numerator coefficients of analog filter object,`Ha`
`getden`	`Den = getden(Ha)`	Get the denominator coefficients of analog filter object, `Ha`
`getgain`	`G = getgain(Ha)`	Get the gain of analog filter object, `Ha`
`refspectrum`	`y = refspectrum(Ha)`	Sets the reference magnitude spectrum to, `Ha`

Loading an external coefficient datafile

You may import a vector of data/coefficients into FilterScript via the importdata function:

h=importdata(Filename)

Where, Filename must be the full pathname and filename entered in quotes, e.g.

h=importdata("c:Tempmysteryfilter.txt");

All data is read on a line by line basis. This allows for multiple entries per line that are delimitated by a comma.
Complex data may be imported by using the i or j keyword.
A maximum of 512 values may be imported.
Comments may be placed anywhere, and must be preceded with the //

General syntax and data manupilation

General syntax and data manipulation

Function	Description
`General`	All variables may contain upper and lower case characters, and numbers. e.g. `Num1, myGain, alpha15`
`Interface Variables`	The `interface` keyword must be used to define all interface variables.
Matrices	A generalised matrix is defined as `A(rows,columns)`. Although matrix assignment is not supported, certain vector operations may result in a matrix result, e.g. the vector multiplication: `A=a*transpose(a)`. All data indexes run from `0...N`, you may access a matrix element at row `R` and column M as: `y=A(R,M).` However, you may also access a range of values using the : keyword, e.g. `Y=A(3:5,1:2)` which produces a new matrix Y. For modifying a value of a matrix/vector, use the `eldef` function, e.g. `a(2,1)=eldef(5)`
Vector assignment	By default, a vector is defined as an array with multiple rows and one column. It may contain expressions, variables and constants and must be enclosed in braces { } with comma delimitation. Example: `b = {1,0,3.4,0,1}`; Example: `A = {1,-2cos(TwoPifc/fs),1}`;
Vector manipulation	In order to accommodate transposed vectors, all vectors are defined as a generalised matrix, i.e. `A(rows,columns)`. By default, a vector of length N is defined as `A(N,1)`, whereas a transposed vector is defined as `A(1,N)`. As all data indexes run from `0...N`, you may access vector element `M` as: `y=A(M,0)`. However, you may also access a range of values using the : keyword, e.g. `y=A(3:5,0)`. For modifying a value of a vector, use the `eldef` function. Example `a = {1,0,3.4,0,1}`; // assign five elements to vector a `a(2,0)=eldef(5)`; // set element three to 5 `y=a(0,0)`; // get element zero and assign it to y
Data series	A real valued data series can be created with the following syntax: `y = series(min,step,max)` where, step represents the step size between min (minimum) and max (maximum). Example `a=series(-12,1,1.2);`
User comments	All user comments must be preceded with the`//` keyword. Where, the `/* */` syntax is not supported.

System variables and reserved constants

There are several system variables and constants which can be used in every script and expression.

System variables and reserved constants

Variable	Description
`fs`	The `fs` variable specifies the system sampling frequency in Hz, i.e. `50MHz` is given as `50e6`
`fsunits`	Returns the sampling frequency units, e.g. `500kHz` would return `1e3` for kHz
`Ts`	The `Ts` variable specifies the system sampling period Ts=1/fs
`pi`	`3.14159265358979`
`Twopi`	`6.28318530717959`
`i`	Complex number token, \( sqrt{-1}\)

Mandatory & action keywords

Mandatory keywords

Variable	Description
`Main()`	`Main()` is used to seperate the initialisation code from the “main” code – see the getting started guide for more information.
`Den`	`Den` specifies the denominator filter coefficients. This must be a vector or scalar.
`Num`	`Num` specifies the denominator filter coefficients. This must be a vector or scalar.
`Gain`	`Gain` specifies the filter gain. This must be real.

Action keywords

Variable	Description
`ClearH1`	The `ClearH1` keyword will delete the H1 filter from the cascade.
`ShowH2DM`	The `ShowH2DM` keyword will show the H2 design marker specification used with IIR and FIR design functions.
`SkipSC`	The `SkipSC` keyword will skip the pole stability check. This useful when working on oscillators and integrators.
`H1Num`	The `H1Num` keyword sets the H1 numerator coefficients
`H1Den`	The `H1Den` keyword sets the H1 denominator coefficients.
`H1Gain`	The `H1Gain` keyword sets the H1 filter gain.

ASN FilterScript – Reference guide

Trigonometrical functions

Vector functions

General functions

Math operators

IIR filter design methods

FIR filter design methods

Analog -> digital filter design: Laplace transforms

Loading an external coefficient datafile

General syntax and data manupilation

System variables and reserved constants

Mandatory & action keywords

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