Signal transfer function

Signal transfer function

The signal transfer function (SiTF) is a measure of the signal output versus the signal input of a system such as an infrared system or sensor. [cite book | title = The Optical Transfer Function of Imaging Systems | author = Tom L. Williams | publication = CRC Press | year = 1998 | isbn = 0750305991 | url = http://books.google.com/books?id=-luzt97NKLEC&pg=PA247&dq=SiTF+signal-transfer-function+input-and-output&as_brr=3&ei=aW_tSMW0LY32sgPz_Y2YBw&sig=ACfU3U2RiRXiIsqTURSS6Uo-qUm2ACGKrA ]

SiTF evaluation

In evaluating the SiTF curve, the signal input and signal output are measured differentially; meaning, the differential of the input signal and differential of the output signal are calculated and plotted against each other. An operator, using computer software, defines an arbitrary area, with a given set of data points, within the signal and background regions of the output image of the infrared sensor, i.e. of the Unit Under Test (UUT), (see "Half Moon" image below). The average signal and background are calculated by averaging the data of each arbitrarily defined region. A second order polynomial curve is fitted to the data of each line. Then, the polynomial is subtracted from the average signal and background data to yield the new signal and background. The difference of the new signal and background data is taken to yield the net signal. Finally, the net signal is plotted versus the signal input. The signal input of the UUT is within its own spectral response. (e.g. color-correlated temperature, pixel intensity, etc.). The slope of the linear portion of this curve is then found using the method of least squares. [Electro Optical Industries, Inc.(2005). EO TestLab Methodology. In "Education/Ref". http://www.electro-optical.com/html/toplevel/educationref.asp.]

SiTF calculations

The average signal and background are calculated by the following equations:

:mu,Sig_{ave} = frac{sum_{i=o}^n X_i}{n} qquad qquad mu,Background_{ave} = frac{sum_{i=0}^p Y_i}{p}

:where :n, = the number of lines in the target area X, or Y,:p, = the horizontal pixel resolution in the target area X, or Y,:i, = the i,th line or horizontal pixel resolution in the target area X, or Y,:X, = an arbitrarily defined area in the illuminated portion of the image (signal region).:Y, = an arbitrarily defined area in the non-illuminated portion of the image (background region).

A second order polynomial is calculated using a double summation:

:f(X)_i = sum_{j=0}^m sum_{i=0}^n a_j X_i^j qquad qquad f(Y)_i = sum_{j=0}^m sum_{i=0}^n a_j Y_i^j:f, = the output sequence best fit:X, = the input sequence (signal region):Y, = the input sequence (background region):a, = the polynomial fit coefficient:m, = the polynomial order

The second order polynomial is subtracted from the original data and the mean is taken:

:mu,Sig = mu,Sig_{ave} - f(X)_i qquad qquad mu,Background = mu,Background_{ave} - f(Y)_i

Then, the net signal is calculated:

:Signal = mu,Sig - mu,Background

SiTF curve

The SiTF curve is then given by the signal output data, (net signal data), plotted against the signal input data (see graph of SiTF to the right). All the data points in the linear region of the SiTF curve can be used in the method of least squares to find a linear approximation. Given n, data points (x_i,,y_i,) a best fit line parameterized as y = mx + b, is given by: [Aboufadel, E.F., Goldberg, J.L., Potter, M.C. (2005)."Advanced Engineering Mathematics (3rd ed.)."New York, New York: Oxford University Press]

: m = frac{frac{sum x_iy_i}{n} - frac{sum x_i}{n} frac{sum y_i}{n{frac{sum x_i^2}{n}-(frac{sum x_i}{n})^2} qquad qquad b = frac{sum y_i}{n} - m frac{sum x_i}{n}

See also

* Optical transfer function
* Signal-to-noise ratio
* Distortion
* Minimum resolvable temperature difference
* Noise equivalent temperature difference
* Power spectral density
* Minimum resolvable contrast
* Signal to noise ratio (image processing)

References

External links

* http://www.electro-optical.com/html/


Wikimedia Foundation. 2010.

Игры ⚽ Нужна курсовая?

Look at other dictionaries:

  • Transfer function — A transfer function (also known as the system function[1] or network function) is a mathematical representation, in terms of spatial or temporal frequency, of the relation between the input and output of a linear time invariant system. With… …   Wikipedia

  • Optical transfer function — The optical transfer function (OTF) of an imaging system (camera, video system, microscope etc) is the true measure of resolution (image sharpness) that the system is capable of. The common practice of defining resolution in terms of pixel count… …   Wikipedia

  • Signal Transfer Point — A Signal Transfer Point (STP) is a router that relays SS7 messages between signaling end points (SEPs) and other signaling transfer points (STPs). Typical SEPs include SSPs and SCPs. The STP is connected to adjacent SEPs and STPs via signaling… …   Wikipedia

  • Modulation transfer function (infrared imaging) — The Modulation Transfer Function (MTF) is used to approximate the position of best focus of an infrared imaging system. In an imaging system, best focus is typically achieved when the MTF is between 0.4 and 0.6; most often at 0.5 (50% cutoff… …   Wikipedia

  • Head-related transfer function — The head related transfer function HRTF , also called the anatomical transfer function ATF , describes how a given sound wave input (parameterized as frequency and source location) is filtered by the diffraction and reflection properties of the… …   Wikipedia

  • Closed-loop transfer function — A closed loop transfer function in control theory is a mathematical expression (algorithm) describing the net result of the effects of a closed (feedback) loop on the input signal to the circuits enclosed by the loop. Contents 1 Overview 2… …   Wikipedia

  • loop transfer function — noun The ratio of the Laplace transform of the primary feedback signal of a control system to that of the actuating signal Syn: loop ratio …   Wiktionary

  • Signal to noise ratio (image processing) — The Signal to Noise Ratio (SNR) is used in image processing as a physical measure of the sensitivity of an imaging system. Industry standards measure SNR in decibels (dB) and therefore apply the 20 log rule to the pure SNR ratio. In turn,… …   Wikipedia

  • Signal (bridge) — In the card game of contract bridge, partners defending against a contract may play particular cards in a manner which gives a signal or coded meaning to guide their subsequent card play; also referred to as carding. Contents 1 Standard signals 1 …   Wikipedia

  • function — 1. The special action or physiologic property of an organ or other part of the body. 2. To perform its special work or office, said of an organ or other part of the body. 3. The general properties of any substance, depending on its chemical …   Medical dictionary

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”