Index

Accumulators, 101

Adaptation, 57, 61, 63

Adaptive, 56, 61, 64

digital notch filter, 64, 65

Adder, 101, 106–111, 118

Akaike, 69

Aliasing error, 14

Amplitude, 23, 45, 61, 64, 75

statistics, 35, 36

Analogue, 11–12

comparator, 103

form, 101, 104

lowpass filter, 14

memory, 16, 17

multiplexer, 56

signal, 1, 11, 12, 101, 119, 161

systems, 125

to digital converter, 14, 101, 103, 106, 129

Antenna, 105

APF, 54–58

ARMA, 10, 48

Associative, 24

Autoregressive, 10

System, 114

Ballistic, 33

Band-limited

additive signals, 3

Signal, 14

BFSK, 64

Binary, 24, 38, 41–43, 104

frequency shift key, 64

Bit, 41–43

Blinkers, 121

Butterfly diagrams, 99, 155

Butterworth, 58

Central limit theorem, 33

Characteristic, 43

Commutative, 24

Complementary function, 32

Complex, 50, 69

all-pass filter, 55

coefficient, 50, 78, 82, 141

conjugate poles, 114

pole filter, 54

poles, 54

spectrum, 89

vector, 98

Composite signals, 4

Conjugate symmetry, 30

Continuous, 1, 5

domain, 29

random variable, 32

systems, 26, 27, 29

time domain, 6, 8

variable, 82

Convergent, 23

conversion unit, 16

Converters

A/D, 16

flash, 103

sigma–delta, 104

synchro-to-digital, 105

Convolution, 24, 25, 89, 90

circular, 90, 91, 99, 155

operator, 25

Correlation

autocorrelation function, 25, 26, 32, 35, 43, 134

function, 25

operation, 24, 25

D/A converter, 103

Decimal numbers, 41

Decimation, 83, 85, 86, 88

Demodulation, 64

DF, 77

DFT, 79

Difference equation, 23, 27, 32

Digital, 11, 15

converter, 14, 15

filter, 19, 28, 38

form, 2

receivers, 14

signal, 11

signal processing, 19, 21

to analogue converter, 103

Digitisation, 11

Direction

directional receiver, 123

finding system, 68

of arrival, 122

Discrete, 1, 5, 7, 12, 15

curve, 23

domain, 5, 17, 23, 29, 30

form, 16

Fourier transform, 6, 8, 25, 36, 78, 79, 81, 83, 141

random variable, 32

signal, 1, 12, 16, 32

spectrum, 12

system, 30, 32

time, 18

time domain, 6, 8, 17, 71

time signal, 12

time systems, 7, 8

DoA, 122

DSP, 19, 20, 69, 79, 101

algorithms, 19

processor, 2, 19, 101, 113, 129

Dynamic, 43

Embedded, 66

Engineering, 121

Exponent, 43

FDLS, 95

FFT, 79, 88, 90, 99, 113, 155

chipset, 113

Figure-of-eight, 125

Filter, 45

adaptive, 63, 64, 67

all-pass filter, 54, 55, 68

anti-aliasing, 16, 17

autoregressive, 46, 58

autoregressive moving average, 10, 48

Butterworth, 61

Chebyshev, 61

digital, 2, 19

exponential weighted, 47

fading, 47

FIR, 27, 41, 74, 76, 83

IIR, 27, 48, 78, 109, 161

Kalman, 73, 76, 78

linear phase, 48

moving-average, 46

narrowband, 53

notch, 57, 65

Finite impulse response, 27

Finite state automaton, 34

FIR, 108

Fixed-point

adders, 118

format, 118

hardware, 119, 161

implementation, 106, 118

multiplication, 106

multipliers, 118

numbers, 42

representation, 118

Floating-point, 43

domain, 25

number, 43

Forgetting factor, 66

Forward problem, 45

Fourier

coefficient, 88

fast Fourier transform, 79, 83

series, 6, 12, 50, 88

series coefficient, 88

spectrum, 8, 13

transform, 2, 3, 6, 12, 36, 78, 79, 81, 83

FPGA, 101, 117–119, 161

Frequency

angular, 29, 58, 77

carrier, 3

corner, 46

cut-off, 14, 46, 59

domain, 2, 8, 12, 13, 14, 20, 24, 45, 129

flash, 53

normalised, 17, 53, 66–68

normalised centre, 65

Nyquist, 19, 30, 54

peak, 61

pulse repetition, 3

response, 49, 54, 56, 58, 61

sampling, 16

Frequency domain least squares, 95

Function

autocorrelation, 25

complementary, 32

correlation, 25

criteria, 63

Dirac delta, 12

exponentially weighted, 66

generator, 119

Kronecker delta, 7, 52

logic, 104

multivariate, 37

non-linear, 33

objective, 63

periodic, 6, 88

probability density, 5, 32

rational, 10

rectangular window, 12

sensitivity, 65

square, 80

staircase, 79

transfer, 8, 28

windowing, 12

Gain, 98

Gaussian

distribution, 5

random variable, 5

Geometric progression, 7

Hamming window, 98

Hard limiter, 104

Hardware, 101–103, 105–107, 109, 111, 113, 119, 155, 161

adder, 107

multiplier, 101, 107

Heterodyning, 50, 53

Ideal adder, 108

IIR, 27, 48, 49

Impulse response, 23

In-phase, 9

Instrumental variable, 72

Integrator, 48, 52

Inverse, 121, 127

Moore–Penrose, 40, 127

problems, 45, 69, 71, 72, 78, 121, 141

IV, 72

IV Approximate ML, 72

IVAML, 72

Laplace, 6

transform, 6, 8

Least-squares estimate, 78

Linear, 21, 22, 26

combination, 73

congruential generator, 35, 52

difference equation, 32

phase, 48, 49, 51

regression, 126

regressor, 74

shift invariance, 23

shift invariant, 23

system, 21, 22, 26, 33, 36, 37, 43, 134

LSE, 78

LT, 6

MA, 46–51, 72

Mantissa, 43

Matrix, 83, 88, 95, 99

inversion, 127

multiplication, 83

Maxima, 38

Maximum likelihood, 72

Mean, 37

Minima, 39

Minimum, 57, 63

Monopulse, 123

Monochromatic, 93

Moore, 40, 43, 134

Moore–Penrose pseudo-inverse, 127

Morphing, 11, 16

Moving average, 27

process, 18, 27, 46

Multidimensional variables, 38

Multivariate, 37

Multiplier, 107, 111, 118

NBF, 48, 53, 54, 58

NCO, 53, 54, 58

Newton–Raphson method, 63

Noise, 35–37, 43, 52, 121

Gaussian, 36

generation, 35

power, 15

propagation, 36

uniformly distributed, 35

white gaussian, 35, 36

Non-linear, 21

Non-stationary, 5

Normalised form, 42

Normalised frequency, 17

Numbers

ones complement, 42

sign magnitude, 41

twos complement, 42

Nyquist

frequency, 54

sampling rate, 30

theorem, 17

Oscillator, 82

numerically controlled, 53

Parametric, 8

representation, 9

spectrum, 8, 11

vector, 10, 11

Parseval's theorem, 91

Particular integral, 32

pdf, 36

Periodic, 90

function, 88, 89

periodicity, 5, 12, 79, 88

Phase, 23

delay, 124

detector, 125

distortions, 125

in-phase, 23

minimum, 30

modulations, 125

shift, 97

Pipelining, 107–109, 119, 161

Polar form, 30

Pole, 29

all-pole system, 27

angle, 30

complex pole filter, 54

plot, 30

pole-zero representation, 29

real pole filter, 54

zero plot, 28

zero cancellation, 69

Polygon, 38

Probability density function, 5, 32, 35

Quadrature, 9, 23

Quantisation, 11, 14, 16, 129

error, 14

noise, 15, 16

Quantiser, 15

Random, 21, 32

Ratio test, 23

Real time, 66, 91

Rectangular

form, 30

matrix, 40

pulse, 16

window Function, 12

Recursive, 19

Region of convergence, 7

Register set-up time, 106

Reliability, 34, 43, 133

ROC, 7

Roulette wheel, 32

Sampling, 2, 11, 12, 15

frequency, 16

rate, 17, 27, 29

time, 12, 17, 29, 30, 126

Scaling, 21

SDC,

Sensitivity, 55, 63, 65

Set-up, 106

Shift

invariance, 23

register, 103

shifting property, 24

Sign magnitude, 41

Signal, 1, 2

band-limited, 3, 12, 14, 16

broadband, 2

instrumented, 1

narrowband, 2, 3, 11

one-dimensional, 1

telemetry, 1

two-dimensional, 1

wideband, 3

Signal-to-noise-ratio, 15, 64

Simpson's rule, 46

SIMULINK, 32, 74, 106, 119

SISO, 22

Slew rate, 17

SNR, 15, 64, 67

Spectral energy, 37

Spectrum, 4, 8,

analyser, 23, 79, 80

discrete, 12

Fourier, 8, 13

heterodyne spectrum analyser, 79

Leonardo, 118

narrowband, 12

non-parametric, 8

non-rectangular windowed, 84

parametric, 8, 11, 95

power, 9, 25, 26, 36

signal, 79

vector, 92

Stability, 23

Stable, 46, 48, 61, 62

Staircase, 80, 95

State transition matrix, 77

Static, 5

Steady state, 95–97

Successive approximation, 17

Superposition, 21, 24

Switch, 16, 17

Symmetric, 11, 17

Synchronising register, 108

Synthesis, 38, 119

Target motion analysis, 72

TMA, 72

Transfer function, 28, 48

Transfer function analyser, 23

Trapezoidal rule, 46

Tustin, 27

Twiddle, 86

UD, 14

ULA, 76

Uncorrelated

zero mean, 74, 76

Uniform linear array (ULA), 76

Uniformly distributed, 14, 52

noise, 35

random number, 14

signal, 15

Unit sample response, 23

Variance, 5, 15, 37

Vectors, 38

WGN, 35

White Gaussian noise, 94

Wiener-Khinchein, 26

Windowing, 11

Word, 41, 43

z-transform, 6

Zero, 32, 42, 48, 53, 54

mean, 64