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In mathematics, a negative number represents an opposite. In the real number system, a negative number is a number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset. If a quantity, such as the charge on an electron, may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative. Negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. The laws of arithmetic for negative numbers ensure that the common-sense idea of an opposite is reflected in arithmetic. For example, −(−3) = 3 because the opposite of an opposite is the original value. Negative numbers are usually written with a minus sign in front. For example, −3 represents a negative quantity with a magnitude of three, and is pronounced "minus three" or "negative three". To help tell the difference between a subtraction operation and a negative number, occasionally the negative sign is placed slightly higher than the minus sign (as a superscript). Conversely, a number that is greater than zero is called positive; zero is usually (but not always) thought of as neither positive nor negative. The positivity of a number may be emphasized by placing a plus sign before it, e.g. +3. In general, the negativity or positivity of a number is referred to as its sign. Every real number other than zero is either positive or negative. The non-negative whole numbers are referred to as natural numbers (i.e., 0, 1, 2, 3...), while the positive and negative whole numbers (together with zero) are referred to as integers. (Some definitions of the natural numbers exclude zero.) In bookkeeping, amounts owed are often represented by red numbers, or a number in parentheses, as an alternative notation to represent negative numbers. It has been proposed that negative numbers were used on the Greek counting table at Salamis, known as the Salamis Tablet, dated to 300 BC.
[2]Paolo Prandoni, [3]LCAV, EPFL
The concept of "basis" for a vector space is one of the most profound
and fruitful ideas in linear algebra. Basis vectors are the "building
blocks" that all other vectors are built from; by "disassembling" a
vector into a linear combination of basis elements we are able to "look
inside" the vector and highlight many of its relevant features.
A vector space has an infinite number oShift + Enter or Ctr + Enter.
As the variables conta [2]Paolo Prandoni, [3]LCAV, EPFL
The Karplus-Strong algorithm is a simple method to generate synthetic
sounds with arbitrary pitch. In this notebook we will explore a few
variations of the method to illustrate some basic notions of
discrete-time signal processing.
In [1]:
%matplotlib inline
import matplotlib
import matplotlib.pyplot as plt
import numpy as np
import IPython
In [2]:
plt.rcParams["figure.figsize"] [2]Paolo Prandoni, [3]LCAV, EPFL
In this notebook we will look at the practical issues associated to
plotting the DFT and in particular the DFT of real-world signals. We
will examine how to map the DFT coefficients to real-world frequencies
and we will investigate the frequency resolution of the DFT and the
effects of zero padding.
In [1]:
[2]Paolo Prandoni, [3]LCAV, EPFL
The Parks-McClellan (PM) algorithm is a clever application of advanced
polynomial fitting techniques to the problem of FIR filter design. In
this notebook we will explore the key ideas behind the method by
considering the design of a simple Type-I lowpass filter.
NOTE: This notebook uses interactive widgets. If the interactive
controls do not work or show up, please fo