signal is transmitted at reduced power. ASK system can be divided into three blocks. The first one represents the transmitter, the second one is a linear model of the effects of the channel, the third one shows the structure of the receiver. The following notation is used: ht(f) is the carrier signal for the transmission hc(f) is the impulse response of the channel n(t) is the noise introduced by the channel hr(f) is the filter at the receiver L is the number of levels that are used for transmission Ts is the time between the generation of two symbols Different symbols are represented with different voltages. If the maximum allowed value for the voltage is A, then all the possible values are in the range [−A, A] and they are given by: the difference between one voltage and the other is: Considering the picture, the symbols v[n] are generated randomly by the source S, then the impulse generator creates impulses with an area of v[n]. These impulses are sent to the filter ht to be sent through the channel. In other words, for each symbol a different carrier wave is sent with the relative amplitude. Out of the transmitter, the signal s(t) can be expressed in the form: In the receiver, after the filtering through hr (t) the signal is: where we use the notation: where * indicates the convolution between two signals. After the A/D conversion the signal z[k] can be expressed in the form: In this relationship, the second term represents the symbol to be extracted. The others are unwanted: the first one is the effect of noise, the third one is due to the intersymbol interference. If the filters are chosen so that g(t) will satisfy the Nyquist ISI criterion, then there will be no intersymbol interference and the value of the sum will be zero, so: the transmission will be affected only by noise. Probability of error The probability density function of having an error of a given size can be modelled by a Gaussian function; the mean value will be the relative sent value, and its variance will be given by: where is the spectral density of the noise within the band and Hr (f) is the continuous Fourier transform of the impulse response of the filter hr (f). The probability of making an error is given by: where, for example, is the conditional probability