Signals and systems - Biomedical Engineering Desk Reference - page 76

3. In the system given in Problem 2.3.2, the input is
changed to a signal that smoothly goes from 0.0 to 5.0
in 10 seconds [i.e., In(t) ¼ 0.5t seconds]. What will
the output look like? ( Note: G and H are simple
constants, so Eq. 2.3.7 still holds.)
4. A resistor produces 10- m V noise when the room
temperature is 310 K and the bandwidth is 1 kHz.
What current noise would be produced by this
resistor?
5. The noise voltage out of a 1-M U resistor is measured
using a digital volt meter as 1.5 m V at a room
temperature of 310 K. What is the effective
bandwidth of the voltmeter?
6. If a signal is measured as 2.5 V and the noise is 28 mV
(28 10 3 V), what is the SNR in decibels?
7. A single sinusoidal signal is found in a large amount of
noise. (If the noise is larger than the signal, the signal
is sometimes said to be 'buried in noise.') The RMS
value of the noise is 0.5 V and the SNR is 10 dB.
What is the RMS amplitude of the sinusoid?

given of the early use of an electric circuit model to
represent the cardiovascular system and an early me-
chanical model of skeletal muscle.
All signals are contaminated by noise, variability, or
other artifact. Efforts to obtain meaningful information
from physiological processes are often thwarted by the
inability to directly measure variables of interest. All too
frequently variables only loosely related to the process of
interest are readily available, and these may be altered by
the physiological process itself or the influence of other
processes. The measurement device, the biotransducer,
is often a major source of measurement errors because it
responds to influences of other energy forms or envi-
ronmental factors. Finally, all electrically based mea-
surements are contaminated by thermal and/or shot
noise. These two noise processes are well defined and
contain noise energy over a wide range of frequencies.
This broad distribution of energy means that thermal and
shot noise can always be improved by limiting the
frequencies contained in the signal. A variety of filters
exist in analog and digital forms to limit the frequencies
in a signal to only those that carry the desired

information.

MATLAB problems
8. Use the approach presented in Example 2.3.3 to
determine if either of two processes, process_y or
process_z, are linear. The two processes are found
on the disk as MATLAB functions.
9. Write a MATLAB function that takes in two vari-
ables, and input variable x and gain variable G, and
produces and output variable y . This function should
implement the feedback equation (Eq. 2.3.7), with
the variable H set to 1.0 (i.e., a unity gain feedback
system). (Name the function 'fbk_system.')
Input a two-cycle sine wave as in Example 2.3.3
having an amplitude of 1. Plot the maximum values
of the input-output relationship for this process [i.e.,
max (y)/max (x)] as a function of G , where G
ranges between 1 and 1,000. ( Hint: Put the process
in a for-loop as in Example 2.3.3 and increment G .
This will provide a more detailed demonstration of
the relationship between the input-output ratio and
the importance of the value of G in a feedback
system.)

Problems
1. An electrical inductor has a defining equation that is
the same as a mass if the variable voltage and current
are substituted for force and velocity (specifically,
V L ¼ L di/dt). A constant voltage of 10 V is placed
across a 1-H inductor. How long will it take for the
current through the inductor to reach 1 A? (See
Example 2.3.2.)
2. Assume that the feedback control system presented
in Example 2.3.4 is in steady-state or static
conditions. If G ¼ 100 and H¼ 1 (i.e., a unity gain
feedback control system), find the output if the input
equals 1. Find the output if the input is increased to
10. [Note how the output is proportional to the
input, which accounts for why a system (having this
configuration) is sometimes termed a proportional
control system. ] Now find the output if the input is
10 and G is increased to 1,000. Note that the
difference between the input and output values
depends on the value of G.