The invention relates to a spectrum analysis method and apparatus. The spectrum analysis method comprises the steps: the step 1, setting the value of a parameter T, N, f1f2...fN, Epsilon 0, Epsilon 1, Epsilon2,..., and Epsilon N, and setting the initial value of a bias component s0, a sine component s1, s2, ..., sN and the initial value of a cosine component c1, c2, ..., cN; the step 2, setting initial value of a bias component increment k1(0), a sine component increment k1(1), k1(2), ..., k1(N), the initial value of a cosine component increment k(-)1(1), k(-)1(2), ..., k(-)1(N); the step 3, successively reading sampling data, and utilizing an iterative method to perform decomposition processing for the sampling data h(s); and the step 4, repeating the step 3 until completing decomposition processing of all the sampling data, and performing spectrum analysis. The spectrum analysis apparatus is simple in structure and is small in operand, and reduces consumption of memory.