What is a symbolic expression (syms) and how do I use this when doing differentiation in matlab?

Hi I have some data with voltage spike recordings that I need to count. I want to use the diff() function to count the number of spikes (i.e. the number of rises and drops) that occur over a period of time. However, I am seeing that I need to use a symbolic expression for the thing that I am differentiating with respect to. Can someone explain to me what this means? Can I make an array of symbolic expressions? (For example, an array times that are of type syms)?

Thank you!!!

Answer 1

[John D'Errico]

No. You misunderstand what diff does, and why diff is used there.

diff, when applied to a numeric vector, forms the difference between successive elements. This is NOT a derivative.

For example,

X = primes(20)

X = 1×8

2 3 5 7 11 13 17 19

dx = diff(X)

dx = 1×7

1 2 2 4 2 4 2

All it did was compute the difference between pairs of successive elements. We can get the same result by the operation:

dx_2 = X(2:end) - X(1:end-1)

dx_2 = 1×7

1 2 2 4 2 4 2

Again, this is NOT a derivative. Your confusion stems from the fact that diff can also be used to perform differentiation, when applied to a symbolic expression. And that is where syms comes in. For example:

syms x
whos x

  Name      Size            Bytes  Class    Attributes

  x         1x1                 8  sym                

So x is a symbolic variable. It contains no numerical value here.

y = x^3 + 3*x^2 - 2

y = 

diff(y,x)

ans = 

As you can see, differentiation of an expression was performed. In both cases, a function named diff was used, but they do entirely different things, depending upon the input arguments.

Answer 2

[Chunru]

If you have numerical recordings instead of fumula/expressions for input, the should use numerical diff. "findpeaks" may be also helpful.

[Victoria Helm]

What is the function for numeric differentiation?

[Chunru]

The function name is same for both symbolic and numerical:

a = rand(8, 1 )

a = 8×1

0.9286 0.9374 0.5973 0.5671 0.1409 0.2975 0.7340 0.3726

b = diff(a)

b = 7×1

0.0088 -0.3401 -0.0302 -0.4262 0.1566 0.4365 -0.3614

[Walter Roberson]

For numeric derivative estimation, typically using gradient() is a better choice.

Numeric differences can be estimated in several different ways. Forward differences; Backwards Differences; Central Differences; and others.