By Margaret Cheney, Brett Borden

ISBN-10: 0898716772

ISBN-13: 9780898716771

Radar imaging is a mathematically wealthy topic with many fascinating purposes and a wide number of demanding, mathematical open difficulties. The target of this e-book is to supply mathematicians with the history they should paintings within the box, construction at the beginning of the underlying partial differential equations. the point of interest is on exhibiting the relationship among the physics and the maths and on providing an intuitive mathematical knowing of uncomplicated ideas. The publication features a description of ways a radar procedure works, including the suitable arithmetic; thought that publications the alternative of radar waveforms; derivation of the basics of scattering concept; derivation and dialogue of the picture formation strategy; and a protracted record of present open difficulties. Readers are assumed to be conversant in the Fourier rework. different assumed heritage fabric comprises yes uncomplicated evidence from vector calculus, complicated variables, linear algebra and physics.

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**Fundamentals of Radar Imaging by Margaret Cheney, Brett Borden PDF**

Radar imaging is a mathematically wealthy topic with many fascinating functions and a wide number of demanding, mathematical open difficulties. The aim of this publication is to supply mathematicians with the history they should paintings within the box, development at the beginning of the underlying partial differential equations.

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**Extra resources for Fundamentals of Radar Imaging**

**Example text**

2). Typically waves scatter mainly from objects whose features are on the same scale as the wavelength. In practice, radar signals are always of finite duration and therefore technically cannot have Fourier transforms supported only in a finite frequency band [71]. However, in practice, their energy is very small outside some finite interval of frequencies, which is called the frequency band of the radar system. The length of this interval is called the bandwidth of the system. A more precise definition can be found in many sources [37, 21] but is not needed here.

25 ✐ ✐ ✐ ✐ ✐ ✐ ✐ 26 CBMSbo 2009/8/13 page 26 ✐ Chapter 4. Detection of Signals in Noise We would like to apply a filter to srec in order to improve the signal-to-noise ratio (SNR). 1) where ηs (t) = h(t − t )s(t − τ ) dt ηn (t) = and h(t − t )n(t ) dt . We would like the signal output ηs (τ ) at time τ to be as large as possible relative to the noise output ηn (τ ). We model the noise as a random process. Thermal noise in the receiver is well modeled by white noise, which means that E[n(t)n∗ (t )] = N δ(t − t ), where E denotes expected value and where N is a constant corresponding to the noise power.

We would like the signal output ηs (τ ) at time τ to be as large as possible relative to the noise output ηn (τ ). We model the noise as a random process. Thermal noise in the receiver is well modeled by white noise, which means that E[n(t)n∗ (t )] = N δ(t − t ), where E denotes expected value and where N is a constant corresponding to the noise power. Since the noise is random, so is ηn . Thus the SNR we would like to maximize is |ηs (τ )|2 . 2): 2 E|ηn (τ )|2 = E = h(τ − t )n(t ) dt =E h(τ − t )n(t )dt h(τ − t )n(t )dt ∗ h(τ − t )h∗ (τ − t ) E[n(t )n∗ (t )] dt dt N δ(t −t ) =N h(τ − t ) 2 dt = N |h(t)|2 dt, where in the last line we have made the change of variables t = τ − t and where ∗ denotes complex conjugation.

### Fundamentals of Radar Imaging by Margaret Cheney, Brett Borden

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