The pmf can be estimated (inferred) from the histogram, or it may be deduced by some mathematical technique, such as in the coin flipping example.įigure 2-5 shows an example pmf, and one of the possible histograms that could be associated with it. A histogram is always calculated using a finite number of samples, while the pmf is what would be obtained with an infinite number of samples. The corresponding curve for the underlying process is called the probability mass function (pmf). The histogram is what is formed from an acquired signal. The notion that the acquired signal is a noisy version of the underlying process is very important so important that some of the concepts are given different names. Think a factor of ten for very long signals with the calculations being performed on a general purpose computer. This makes the algorithm much faster than the previously described methods. The strategy of this algorithm is to use these slow operations only on the few numbers in the histogram, not the many samples in the signal.

Analysis of the Log-Normal DistributionĬalculating the mean and standard deviation requires the time consuming operations of addition and multiplication.

Why the Complex Fourier Transform is Used.

Another Look at Fixed versus Floating Point.

Architecture of the Digital Signal Processor.

How DSPs are Different from Other Microprocessors.

Example of a Large PSF: Illumination Flattening.

The Chebyshev and Butterworth Responses.

High-Pass, Band-Pass and Band-Reject Filters.

How Information is Represented in Signals.

Multiplying Signals (Amplitude Modulation).Compression and Expansion, Multirate methods.The Frequency Domain's Independent Variable.The Delta Function and Impulse Response.Examples of Linear and Nonlinear Systems.Static Linearity and Sinusoidal Fidelity.

Histogram maker with median